Kurzgesagt – In a Nutshell 

Sources – Black Hole Universe

Thanks to our experts:

• Dr. Miguel Á. Vázquez-Mozo

University of Salamanca

• Dr. Matt Caplan

Illinois State University

In this video we are going to explore from two different points of view what in technical jargon is called "black hole cosmology", i.e. the (relatively old) question of whether the observable universe could be inside a black hole. On the way, we'll review some standard although not always well-known facts about black hole physics.

The first part of the script is based on the empirical fact that, somewhat intriguingly, the observable universe seems to have the exact size and mass that would be required to make a black hole as big as the observable universe itself.

The second, completely independent proposal we explore is the idea that our Universe could be born from the singularity of a black hole, and that in turn the universe that contains that black hole could be born from a black hole itself. If so, universes in later generations of this process could be better fitted to produce an abundance of black holes, in a sort of “natural selection” towards efficient black hole production.

To keep things simple, we will only consider black holes without electrical charge that and don’t rotate, known as Schwarzschild black holes. 

—You would need to squeeze Earth to the size of a coin for it to turn into a black hole. The Sun needs to be squeezed to the size of a small city to become a black hole.

Follows from the previously mentioned formula for the Schwarzschild radius:

R = 2GM/c2

With values obtained from the NASA data sheet.

#NASA (2022): “Sun Fact Sheet” (retrieved 2024)
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html

#Encyclopaedia Britannica: “Schwarzschild radius” (retrieved 2024)

https://www.britannica.com/science/Schwarzschild-radius

#Toth, Viktor T: “Hawking Radiation Calculator” (used 2024)

https://www.vttoth.com/CMS/hawking-radiation-calculator 

—This is usually how black holes are explained. Stuff becomes super dense and collapses into a black hole. 

Such an explanation is given here: 

#NASA (2024):”Black Hole Basics” (retrieved 2024)

https://science.nasa.gov/universe/black-holes/

Quote: “Black holes are among the most mysterious cosmic objects, much studied but not fully understood. These objects aren’t really holes. They’re huge concentrations of matter packed into very tiny spaces. A black hole is so dense that gravity just beneath its surface, the event horizon, is strong enough that nothing – not even light – can escape. The event horizon isn’t a surface like Earth’s or even the Sun’s. It’s a boundary that contains all the matter that makes up the black hole.”

And here:

#European Space Agency: ”Black holes” (retrieved 2024)
https://www.esa.int/Science_Exploration/Space_Science/Black_holes

Quote:”A black hole is an extremely dense object whose gravity is so strong that nothing, not even light, can escape it.”

—We are ignoring some math here, but all you really need to know is one thing: The larger black holes get, the less dense they are. So really large black holes are kind of thin.

In daily life, density is defined in a pretty straightforward manner as the mass of an object divided by its volume:  ⍴= M/V.

The density we are talking about here is an effective density. It is defined as the total mass of the black hole (M) divided by the total volume inside the event horizon. Since the event horizon is a sphere of radius R, the volume enclosed by this sphere is given by the usual formula V=4𝜋R^3/3, so the effective density is:

⍴=M/(4𝜋R3/3)

It aims to represent a notion of average density for the black hole.

If we plug the formula of the Schwarzschild radius in this definition of effective density, we find that:

⍴=(3c6/ 32𝜋G3) · 1/M2

where the first factor is a constant, and the second decreases with mass. Hence, the effective density of a black hole decreases with its mass.

#Encyclopaedia Britannica: “Schwarzschild radius” (retrieved 2024)

https://www.britannica.com/science/Schwarzschild-radius

—A sun-mass black hole is only about 6 km wide and has a density of about one Himalayan range per cubic meter.
We obtain the weight of the black hole using the formula for the Schwarzschild radius:

R = 2GM/c2,

We then divide the  expression by the cubic radius (R3) and rearrange the equation to find the effective density (⍴=M/(4𝜋R3/3)). 

The result is that such a black hole would have a density of  about 1.8·1019 kg/m3. That is, every cubic meter contains, on average, 1.8·1019 kg of black hole mass.

#Toth, Viktor T: “Hawking Radiation Calculator” (used 2024)

https://www.vttoth.com/CMS/hawking-radiation-calculator 

The Himalayan mountain range has an area of 595,000 km2,

#Encyclopaedia Britannica: “Himalayas” (retrieved 2024)

https://www.britannica.com/place/Himalayas 

Quote: “[The Himalaya’s] total area amounts to about 230,000 square miles (595,000 square km).”

or equivalently, 5.95·1011 m2. An estimate of its average height depends on where you want to measure that height from, and it could reasonably range from 5,000 m to 7,000 m. Some estimations of the height of the Great Himalayas, the highest part of the mountain range, place 6,100 m as a lower limit on its average height. Since it is a lower limit of the highest part of the range, we will take it as an average for the whole mountain range.

#Encyclopaedia Britannica: “Great Himalayas” (retrieved 2024)

Quote: “Great Himalayas, highest and northernmost section of the Himalayan mountain ranges.[...]The range’s total length is some 1,400 miles (2,300 km), and it has an average elevation of more than 20,000 feet (6,100 metres).“

https://www.britannica.com/place/Great-Himalayas 

That give us an estimated volume of:

5.95 ·1011 m2  × 6.1 ·103 m = 3.6 ·1015 m3.

Then, multiplying by the average density of rock (2.6·103  kg/m3), we obtain an estimated mass of

3.6 ·1015 m3 × 2.6 ·103 m = 9.4 ·1018 m3,

Which is approximately the mass contained in a cubic meter of or black hole.  

#Jones, Francis H.M. (2018): “Geophysics for Practising Geoscientists; Learning Resources about Applied Geophysics”

https://www.eoas.ubc.ca/courses/eosc350/content/foundations/properties/density.htm 

Quote: “Most of the rocks comprising the crust of the earth have density between 2.6 and 2.7g/cc”

—The supermassive black hole at the center of the Milky Way has a mass of 4 million suns, a diameter of 24 million kilometers, and a density of 6 blue whales per cubic meter. 

We calculate the density of the black hole following the same steps as above. 

The result is that each cubic meter of the black hole at the center of our galaxy contains, on average, 1.15·106 kg of mass, that is, the mass of around  blue whales, each with a weight of 200,000 kg.

#Toth, Viktor T: “Hawking Radiation Calculator” (used 2024)

https://www.vttoth.com/CMS/hawking-radiation-calculator

#NASA (2024):”Black Hole Basics” (retrieved 2024)

https://science.nasa.gov/universe/black-holes/
Quote: “Most Milky Way-sized galaxies have monster black holes at their centers. Our is called Sagittarius A* (pronounced ey-star), and it’s 4 million times the Sun’s mass.”

#Encyclopaedia Britannica: “Schwarzschild radius” (retrieved 2024)

https://www.britannica.com/place/Sagittarius-A-astronomy

Quote: “Sagittarius A* (Sgr A*), supermassive black hole at the centre of the Milky Way Galaxy, located in the constellation Sagittarius and having a mass equivalent to four million Suns.

Sagittarius A* is a strong source of radio waves and is embedded in the larger Sagittarius A complex. Most of the radio radiation is from a synchrotron mechanism, indicating the presence of free electrons and magnetic fields. Sagittarius A* (pronounced “Sagittarius a star”) is a compact, extremely bright point source. X-ray, infrared, spectroscopic, and radio interferometric investigations have indicated the very small dimensions of this region; the event horizon of the black hole has a radius of 12 million km (7 million miles).”

#Whale and Dolphin Conservation: “Facts about blue whales”

https://uk.whales.org/whales-dolphins/facts-about-blue-whales/

Quote: “Female blue whales weigh more (190,000kg) than males (150,000kg). At around 2,700kg newborn blue whale weighs about the same as an adult hippopotamus. The heart of a blue whale can weigh 450kg. Before they were hunted by commercial whaling, some whales reached 200,000kg.”

—The ultramassive black hole IRAS 20100−4156 has a mass of 3.8 BILLION suns and is as wide as a solar system. But because it is so large, it is just as dense as air! 

IRAS 20100-4156 is a rotating black hole,  but we'll treat it as a non-rotating one to keep the math simple and because the exact formulas only change the result by a small factor, which is more than enough for the qualitative comparison we are making. Under this approximation, its Schwarzschild radius can be calculated using the formula mentioned above.  It yields a value of 1.1·1010 km, comparable to the average radius of Neptune’s orbit. 

#Toth, Viktor T: “Hawking Radiation Calculator” (used 2024)

https://www.vttoth.com/CMS/hawking-radiation-calculator 

#NASA Earthdata: “Air Mass/Density” (retrieved 2024)
https://www.earthdata.nasa.gov/topics/atmosphere/atmospheric-pressure/air-mass-density

Quote: “Pure, dry air has a density of 1.293 kg m−3 at a temperature of 273 K and a pressure of 101.325 kPa.”

—This means, at least in theory, that if you take a gigantic balloon and fill it with undecillions of tons of air, the moment it gets to the size of a solar system, an event horizon suddenly forms and it turns into a supermassive black hole. Without violence or squeezing.

From our comment above, a black hole the size of the solar system would have a mass of 3.8 billion suns. Using the value for the mass of the Sun provided by NASA, that makes a total of about 7.6·1039 kg or around 8 undecillion tons. 

#NASA (2022): “Sun Fact Sheet” (retrieved 2024)
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html

However, this is more of a useful visualization than a black hole creation manual: you can’t actually put 8 undecillion tons, and not only because of insufficient balloon manufacturers.  That amount of air would have an appreciable gravity and collapse unto itself before reaching the required mass, and, in fact, if you are going to put that air into a balloon, you probably need to have it close by anyways and definitely inside its Schwarzschild radius, so the black hole would have been already formed.

—The chunk of the universe that we can see from Earth is a sphere with a radius of 45 billion light-years, filled with hundreds of billions of galaxies, lots of gas and a bunch of other things. 

One’s first estimation of the observable universe's size may be that it is 13.4 billion light-years, since we know the Big Bang happened 13.4 billion years ago. However, due to the expansion of space, galaxies that emitted photons in our direction eons ago are now much farther than they were when they emitted those photons, and so, it turns out that we can observe galaxies that are now much more than 13.4 billion light-years away. 

#NASA’s Goddard Space Flight Center (2017): “Age & Size of the Universe Through the Years”(retrieved 2024)

https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/educators/guide/age_size.html 

Quote: “The most distant objects in the Universe are 47 billion light years away, making the size of the observable Universe 94 billion light years across. How can the observable universe be larger than the time it takes light to travel over the age of the Universe? This is because the universe has been expanding during this time.”

The amount of galaxies in the observable universe is calculated from observational data, for example from Hubble, and it has been recently revised to account for prolific galaxy formation in the early Universe. 

#ESA Science and Technology:Hubble (2016): “Observable Universe contains ten times more galaxies than previously thought” (retrieved 2024).

https://sci.esa.int/web/hubble/-/58444-observable-universe-contains-ten-times-more-galaxies-than-previously-thought-heic1620 

Quote: “One of the most fundamental questions in astronomy is that of just how many galaxies the Universe contains. The Hubble Deep Field images, captured in the mid-1990s, gave the first real insight into this. Myriad faint galaxies were revealed, and it was estimated that the observable Universe contains about 100 billion galaxies. Now, an international team, led by Christopher Conselice from the University of Nottingham, UK, have shown that this figure is at least ten times too low.”

#Conselice, Christopher J. et al. (2016): “The evolution of galaxy number density at z < 8 and its implications” The Astrophysical Journal, vol. 830, 83
https://iopscience.iop.org/article/10.3847/0004-637X/830/2/83 

Quote: “Our major finding is that the number densities of galaxies decrease with time such that the number density fT(z) ∼ t−1, where t is the age of the universe. We further discuss the implications for this increase in the galaxy number density with look-back time for a host of astrophysical questions. Integrating the number densities fT, we calculate that there are (2.0 ± 0.7/0.6) galaxies in the universe up to z = 8, which in principle could be observed.”

—If you add them up, it has the mass of about a million billion billion suns. Which sounds a lot – but on average, the universe is not very dense. If we break up all the galaxies, stars, gas and energy, and spread them equally inside the volume of the universe, we get an average density of about 5 hydrogen atoms per cubic meter. You can imagine this as the sort of ultra thin “cosmic air” that makes up the universe.

Our most advanced observational data suggests that the Universe is flat, that is, its spatial curvature is zero. 

#Planck collaboration (2020): “Planck 2018 results: VI. Cosmological parameters.” Astronomy & Astrophysics, vol.641, A6

https://www.aanda.org/articles/aa/full_html/2020/09/aa33910-18/aa33910-18.html

Quote:  “The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002.”

The curvature of the universe is related to its density. A dense enough universe will wrap space unto itself (we call this a spherical or positive curvature universe) while a very sparse universe will keep expanding forever (we call this a hyperbolic or negative curvature space). 

We seem to exist in a universe sitting on the edge of the knife, with just enough curvature to halt the expansion of space in infinite time. Using Friedman’s equations, one can deduce an expression for the density of such a Universe, called the critical density because it is the critical point between an spherical and a hyperbolic Universe. It is:

⍴c=3H2/(8𝜋G)

Where H is the Hubble constant and G is the universal gravitational constant. 

#COSMOS - The SAO Encyclopedia of Astronomy: “Critical density” (retrieved 2024)

https://astronomy.swin.edu.au/cosmos/c/Critical+Density 

Quote: “The ‘critical density’ is the average density of matter required for the Universe to just halt its expansion, but only after an infinite time. A Universe with the critical density is said to be flat. [...] The critical density for the Universe is approximately 10-26 kg/m3 (or 10 hydrogen atoms per cubic metre) and is given by: ⍴c=3H2/(8𝜋G)”

This average density encompasses not only the mass-energy of galaxies and interstellar gas, it includes the mass-energy of dark matter and dark energy.

Given the observed values for H and G the critical density of our Universe turns out to be:

⍴c=8.56·10-27 kg/m3,

Or, in units of the mass of the proton (identical to that of the hydrogen atom for the precision we are working with):

⍴c= 5.13 protons/m3

#Particle Data Group: Reviews Tables & Plots (2023): “Physical constants (rev.)” for the mass of the proton & “Astrophysical constants (rev.)” for the Hubble constant, Gravitational constant. (retrieved 2024)

https://pdg.lbl.gov/2023/reviews/contents_sports.html 

Multiplying this critical density by the volume of the observable universe yields a total mass of the observable Universe of: 

M=⍴c · V= 4𝜋 ⍴c · R3 obs. univ./3=  1.7  ·1024 sun masses

#NASA (2022): “Sun Fact Sheet” (retrieved 2024)
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html

That is, a "million billion billion" (24=6+9+9).

—Well, it turns out that all the mass in the observable universe is more than enough to create a black hole. Actually, it is enough to make a black hole 10 times larger than the observable universe. 

We calculate the Schwarychild radius of the black hole with the mass of the observable universe using the usual formula for the Schwarzschild radius of a black hole of given mass.

#Toth, Viktor T: “Hawking Radiation Calculator” (used 2024)

https://www.vttoth.com/CMS/hawking-radiation-calculator 

As explained at the beginning of this paragraph in the script, the observable universe is around 45 billion light years across, that is, 4.5  · 1010 light years.

#NASA’s Goddard Space Flight Center (2017): “Age & Size of the Universe Through the Years”(retrieved 2024)

https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/educators/guide/age_size.html   

Quote: “The most distant objects in the Universe are 47 billion light years away, making the size of the observable Universe 94 billion light years across. How can the observable universe be larger than the time it takes light to travel over the age of the Universe? This is because the universe has been expanding during this time.”

 Given that the Schwarzschild radius we just calculated is 5.3  · 1011 light years, this means the black hole would be approximately ten times larger than the observable universe.

—There is one catch though. We know that our universe is expanding – and an expanding universe is not what you would expect to see if you were inside a black hole. So our universe can’t be a black hole – at least not in the naive way we’ve just described. 

Our Universe is expanding homogeneously and in all directions.

#NASA (2013): Universe 101: “Tests of Big Bang: Expansion”

https://map.gsfc.nasa.gov/universe/bb_tests_exp.html 

Quote:
“In 1929, Edwin Hubble announced that his observations of galaxies outside our own Milky Way showed that they were systematically moving away from us with a speed that was proportional to their distance from us. The more distant the galaxy, the faster it was receding from us. [...]The specific form of Hubble's expansion law is important: the speed of recession is proportional to distance. [...] 

The expanding raisin bread model at left illustrates why this proportion law is important. If every portion of the bread expands by the same amount in a given interval of time, then the raisins would recede from each other with exactly a Hubble type expansion law. In a given time interval, a nearby raisin would move relatively little, but a distant raisin would move relatively farther - and the same behavior would be seen from any raisin in the loaf. In other words, the Hubble law is just what one would expect for a homogeneous expanding universe, as predicted by the Big Bang theory.”

As it will be discussed in the next few sentences of the script, this is radically opposed to what we expect to see in a black hole, where two “spatial” dimensions shrink and collapse while another stretches. 

There is another reason why a black hole might not form, even if all our previous considerations about the mass of the Universe and its Swarzchild radius are correct. We’ve said that our universe is a sphere 45 billion light-years in radius. But that’s just the observable part – the part that we can see from Earth. Our best cosmological models seem to indicate that the universe goes on far beyond that, and that it might well be infinite and fundamentally the same in all points (“homogeneus”) and directions (“isotropic”). 

#Anselmi et al. What is flat ΛCDM, and may we choose it?. 2022. 

https://arxiv.org/pdf/2207.06547.pdf
Quote: “The Universe is neither homogeneous nor isotropic, but it is close enough that we can reasonably approximate it as such on suitably large scales. [...] Nevertheless, it is common practice to set the parameter that characterizes the spatial curvature, ΩK, exactly to zero. This parameter-fixed ΛCDM is awarded distinguished status as separate model, “flat ΛCDM.””

An universe with critical density, as we have explained ours might be, has zero curvature and infinite size. 

#NASA (2024): Universe 101: “Will the Universe expand forever?”

https://map.gsfc.nasa.gov/universe/uni_shape.html 

Quote:“If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent.”

So if taken literally, the most common interpretation of the standard model of cosmology implies a strictly infinite universe.

In such a case, no matter where you are, you’d have infinite galaxies above you and below you, to your left and to your right. There would be no preferred direction to fall into, and, all points of space being equal, there would be no way to “know” where exactly the black hole should form. To have a cosmic-sized black hole, you’d need to have all the matter in existence concentrated in a region while surrounded by a much bigger vacuum. But this is not what our models of the universe nor our observations say.

—Except there is a wild and mind-bending trick the universe could play on us. To find out how, let us jump into a black hole and die!

Note that, from this moment on, we are addressing a wholly independent black hole cosmology.

—We usually imagine black holes as spheres with a singularity at their center, a point where all their mass is concentrated so much that our math breaks down.

A common notion exemplified here:

#Black hole, Encyclopaedia Britannica, 2024

https://www.britannica.com/science/black-hole#ref190750
Quote: “Black hole, cosmic body of extremely intense gravity from which nothing, not even light, can escape. A black hole can be formed by the death of a massive star. When such a star has exhausted the internal thermonuclear fuels in its core at the end of its life, the core becomes unstable and gravitationally collapses inward upon itself, and the star’s outer layers are blown away. The crushing weight of constituent matter falling in from all sides compresses the dying star to a point of zero volume and infinite density called the singularity.”

However, this picture is misleading. Actually, in the simplest case of a neutral non-rotating black hole, the singularity is a moment in time, not a place in space. 

#Max Planck Institute for Gravitational Physics: “Changing places – space and time inside a black hole”, Einstein Online (retrieved 2024)

https://www.einstein-online.info/en/spotlight/changing_places/   

Quote: “Our analogy is useful in understanding one feature of a black hole singularity that is easy to get wrong. If you hear about a spherically symmetric black hole, bounded by its horizon and containing a central singularity, you are likely to picture a cross-section of the black hole which looks like this:

Here, the circle is meant to represent the horizon, and in the center of the black hole, there is a point – the singularity.

In our three-dimensional model, this picture can be obtained by looking at a plane that is orthogonal to the axis: The intersection of the plane with the horizon-cylinder is a circle, the intersection with the singularity-axis is a point. So is this a snapshot of a black hole, showing its interior structure?

Not quite. Only outside the cylinder does the intersection with a plane at constant height (“at constant time” as seen from the outside) correspond to a snapshot. Inside the cylinder, time and space have switched places. Inside, the intersection image doesn’t show a snapshot – it shows something much more weird: a caleidoscopic combination of many different times. After all, inside, time is not the axial, but the radial coordinate, and all the different distances from the “center” which you see in the sketch correspond to different moments in time. Instead of the spatial structure of the black hole, the sketch shows a strange mix of space and time!

Likewise, if you think about the unstoppable collapse of a body to form a black hole, you might think that the body ends up with all its matter concentrated in a single point of space – the singularity. But again, this picture of the spacepoint-singularity residing in the center of the black hole is simply wrong. Using our analogy, you can see why. The singularity is the whole of the axis – and the axis represents a space direction. Hence, the singularity is not a point in space – it is infinitely extended!”

—From the outside a black hole looks like a normal black sphere.

Here, you can see a simulation of a hypothetical Scharzchild black hole in front of the Milky Way. Since the black hole is Swcharzchild, it looks the same from all angles. 

#Kraus, Ute (2005): “Step by Step into a Black Hole” (retrieved 2024)

https://www.spacetimetravel.org/expeditionsl 

—But the inside is where things stop making sense. Black holes warp the universe so much that, at the event horizon, space and time switch their roles. Inside a normal sphere, space is finite but time goes on forever. But inside a black hole it's the other way around – space goes on forever but time is finite. So once inside, you see an infinite universe with no center.

In general relativity, space and time are connected. They are different sides of a whole space-time, whose geometry is shaped by gravity. An extremely strong gravitational field, like that of a black hole, can distort space-time in surprising and counterintuitive ways. What an observer outside of the black hole understands as a “radial” space coordinate, pointing towards the “center” of the black hole, takes on time-like properties inside the event horizon. That means that, for an observer inside the black hole, a variation in that coordinate is experienced as the passage of time. Likewise, what an observer outside of the black hole experiences as time, turns into a space-like coordinate at the other side of the event horizon, so that an observer within sees it as having an extension, rather than a duration.

Because of this swap, since external observers see the black hole as an object with finite extension and infinite duration, the internal observer finds themselves in an infinite space with finite duration. 

#Max Planck Institute for Gravitational Physics: “Changing places – space and time inside a black hole”, Einstein Online (retrieved 2024)

https://www.einstein-online.info/en/spotlight/changing_places/   

Quote: “From the outside, the region of a black hole looks like the surface of a sphere (in our model with two space dimensions and one time dimension, like the circumference of a circle). But inside that sphere, which has only a finite surface area, you can “hide” objects that are infinitely large – infinitely extended in space. How does this work? Again, it works because time and space trade places. Our simple scenario corresponds to an eternal black hole – a black hole that has always existed and will continue to exist indefinitely in the future. From the outside, the black hole is infinitely extended in time, but has only a finite size in space. Inside, the tables are turned: Time is only of finite extent (it starts at the horizon and ends abruptly at the singularity-axis), but instead one space direction, the axis direction, is now infinitely long.”

#Doran, Rosa; Lobo, Francisco S. N.; Crawford, Paulo.(2007) ”Interior of a Schwarzschild black hole revisited”  Found Phys vol. 38, 160–187 

https://link.springer.com/article/10.1007/s10701-007-9197-6 

https://arxiv.org/abs/gr-qc/0609042 

Quote: “[W]hile for the exterior observer, infalling particles end up at a central singularity at r = 0, from the interior point of view, the proper distance along the z−direction increases, showing the existence of a cigar-like singularity. The latter singularity is a spacelike hypersurface, and the test particles are not directed towards a privileged point, however, in order to not violate causality they are directed along a temporal direction from t = 2ξ to t = 0.”

—The geometry is too complicated, so we are simplifying. But basically you could walk forever in one direction or walk in another direction and arrive at the same place again. 

There are three space-like dimensions inside a black hole. Two of them are like circles: if you  walk along those dimensions, you will eventually find yourself where you started. The third is like an infinite straight line: if you walk along that direction,  no matter how long you manage to walk, there will alway be infinitely more of that direction in front of you. An infinite line of circles one on top of the other is a cylinder, hence this shape is also sometimes called a cylinder. 

#Krasnikov, Serguei. (2008): “Falling into the Schwarzschild black hole. Important details.” Gravit. Cosmol. vol. 14, 362–367 

https://link.springer.com/article/10.1134/S0202289308040129

https://arxiv.org/abs/0804.3619 

Quote: “Thus, an observer after crossing the horizon finds himself in a “universe” with not quite usual properties. The “space” of that universe (i. e., the surface S given in this case by the equation η = const) is a homogeneous cylinder  ℝ1×𝕊2. It is spherically symmetric, but not isotropic, the distinguished direction being that along the l-axis.” 

Another detailed investigation of the geometry inside a Swarzchild black hole is:

#Doran, Rosa; Lobo, Francisco S. N.; Crawford, Paulo.(2007) ”Interior of a Schwarzschild black hole revisited”  Found Phys vol. 38, 160–187 

https://link.springer.com/article/10.1007/s10701-007-9197-6   

https://arxiv.org/abs/gr-qc/0609042  

—But not only that. Inside a black hole time is finite, and it is now running out. So after a while you start to notice that space itself is slowly changing. In one direction space is being stretched, while in all other directions space is shrinking – the whole universe is being squeezed, kind of turning into a collapsing spaghetti.

Inside the black hole, the geometry of space changes with time. The circle-like directions we talked about above shrink, so that, at every instant, the circle you could potentially trace along them becomes smaller, until it finally collapses when the radius becomes zero, which happens after a finite amount of time. All the while, the line-like direction stretches to infinity. 

#Doran, Rosa; Lobo, Francisco S. N.; Crawford, Paulo.(2007) ”Interior of a Schwarzschild black hole revisited”  Found Phys vol. 38, 160–187 

https://link.springer.com/article/10.1007/s10701-007-9197-6 

https://arxiv.org/abs/gr-qc/0609042 

Quote: “Now, allowing for the coordinate to flow backwards from t = 2ξ to t = 0, proper time as measured by observers, at rest relatively to the (z, φ, θ) coordinate system, inexorably runs forward from τ = πξ to τ = 2πξ. For this case, observers move apart along the z−direction and collapse along the angular coordinate”.

—Sooner or later, the whole black hole universe collapses into itself. All of space, every single part of it, is turning into a singularity. So the singularity of a black hole is not at its center or in any direction at all. It is in the future of whatever falls inside.  We made a whole video on this if you want to learn more. 

So the singularity is not a place where you can go – it is an event in time that happens. Once it happens, you and everything else that fell inside the black hole will be mercilessly crushed into an infinitely small region with infinite gravity and infinite energy. Time, space, none of it matters anymore, both kind of stop existing in ways that we would recognize. 

As mentioned above, the idea of the singularity as a point “at the center of the black hole” is a common misconception. The singularity is in fact a moment in time as experienced by an observer inside the black hole. 

#Max Planck Institute for Gravitational Physics: “Changing places – space and time inside a black hole”, Einstein Online (retrieved 2024)

https://www.einstein-online.info/en/spotlight/changing_places/    

Quote: “This is exceedingly weird. From the outside, the region of a black hole looks like the surface of a sphere (in our model with two space dimensions and one time dimension, like the circumference of a circle). But inside that sphere, which has only a finite surface area, you can “hide” objects that are infinitely large – infinitely extended in space. How does this work? Again, it works because time and space trade places. Our simple scenario corresponds to an eternal black hole – a black hole that has always existed and will continue to exist indefinitely in the future. From the outside, the black hole is infinitely extended in time, but has only a finite size in space. Inside, the tables are turned: Time is only of finite extent (it starts at the horizon and ends abruptly at the singularity-axis), but instead one space direction, the axis direction, is now infinitely long.”

The clearest way to see this is with the help of a “Penrose diagram”, an abstract representation of the spacetime around a black hole widely used by physicists. The details are complicated, but the only thing we need to know is that, in these diagrams, time is always the vertical axis, space (the radial coordinate) is always the horizontal axis, and light rays always travel at 45 degrees. For a neutral and not rotating black hole, the Penrose diagram looks like this:

#Hamilton, A.: “Penrose diagrams”. JILA – University of Colorado Boulder & NIST
https://jila.colorado.edu/~ajsh/insidebh/penrose.html 

Quote: “A Penrose diagram is a kind of spacetime diagram arranged to make clear the complete causal structure of any given geometry. They are an indispensable map for navigating inside a black hole. Roger Penrose, who invented this kind of diagram in the early 1950s, himself calls them conformal diagrams.

In a Penrose diagram:

• Light rays move at 45o from the upward vertical;

• Points at infinity (at infinite distance, or in the infinite past or future) are contained in the diagram.”

The event horizon of the black hole is the diagonal line labeled “horizon”. Below that line we find the outside universe, and above that line we find the inside of the black hole. Once inside the black hole, it’s trivial to see why not even light can escape – because it moves at 45º. Any other objects move slower than light and therefore with an angle of more than 45º with the horizontal, so they also cannot exit the horizon and will always end in the singularity. The singularity is the extended wiggly line at the top. Since time runs along the vertical direction, such a horizontal line marks a moment in time: the moment where time itself ends. Time ends there because the diagram ends there: there’s nothing above the singularity. Also apparent in the diagram is the fact that, to escape the singularity, an infalling observer would have to stop time and travel to the past.

—This collapse of the black hole universe into a singularity looks like one of the scenarios for the end of our universe: The Big Crunch, where long after the Big Bang the whole universe collapses into a singularity again. But if there is a Big Crunch, there might be a Big Bounce – like a rubber ball that you’ve squeezed too much and that suddenly rebounds, space might expand again. 

The Big Crunch is one of the possible scenarios for the end of the Universe. In particular, it is the case for a Universe denser than its critical density or, equivalently, a universe of positive curvature. In this scenario, the expansion of the Universe stops and reverses until all space-time, matter and energy collapse in a singularity. 

#COSMOS - The SAO Encyclopedia of Astronomy: “Big Crunch” (retrieved 2024)

https://astronomy.swin.edu.au/cosmos/B/Big+Crunch 

Quote: “The ‘Big Crunch’ is the rather fanciful name given to one of the possible fates of the Universe. In this scenario, the current expansion of the Universe ultimately slows, stops and then reverses to begin contracting. In a time-reversed version of the Big Bang, the contraction eventually compresses the whole of spacetime (and all the matter within it) into a single small region.

For the Universe to end in a Big Crunch it must have sufficient mass to halt and reverse the current expansion. In other words, the density of the Universe must exceed the critical density. Astronomers express this requirement as Ω0 > 1, where Ω0 is the density parameter.”

The endpoint of a Big Crunch has been discussed by cosmologists over the years. According to general relativity, the endpoint should be a singularity similar to the one at the center of a black hole or the one that was supposed to give rise to the Big Bang: a “point of infinite density” at which the theory loses its predictive power. However, physicists think that before reaching an actual singularity, the (as yet unknown) quantum effects of gravity will come into play, which may restart a new phase of expansion:

#Mack, Katie (2020): The End of Everything: (Astrophysically Speaking). Simon & Schuster

https://www.simonandschuster.com/books/The-End-of-Everything/Katie-Mack/9781982103552 

https://www.sciencefriday.com/articles/end-of-everything-excerpt/  (excerpt)

Quote: “A collapsing universe will, in the final stages, reach densities and temperatures beyond what we can produce in a laboratory or describe with known particle theories. The interesting question becomes not “Will anything survive?” (because by this point it is very clear that the answer to that is a straightforward No), but “Can a collapsing universe bounce back and start again?”

Cyclic universes that go from Bang to Crunch and back again forever have a certain appeal in their tidiness. Rather than a beginning from nothing and catastrophic, final end, a cycling universe can in principle bounce along in time arbitrarily far in each direction, with endless recycling and no waste.

Of course, like everything in the universe, it turns out to be significantly more complicated. Based purely on Einstein’s theory of gravity, general relativity, any universe with a sufficient amount of matter has a set trajectory. It starts with a singularity (an infinitely dense state of spacetime) and ends with a singularity. There isn’t really a mechanism in general relativity to transition from an end-singularity to a beginning one, however. And there is reason to believe that none of our physical theories, general relativity included, can describe the conditions of anything close to that kind of density. We have a pretty good understanding of how gravity works on large scales, and for relatively (ha!) weak gravitational fields, but we have no idea how it works on extremely small scales. And the kinds of field strengths you’d encounter when the entire observable universe is collapsing into a subatomic dot are all kinds of incalculable. We can be fairly confident that for that particular situation, quantum mechanics should become important and do something to make a mess of things, but we honestly don’t know what.”

We have covered the topic of the Big Crunch and other possible ends to our Universe in another video:

#Kurzgesagt – In a Nutshell (2014): “Three Ways to Destroy the Universe”

https://www.youtube.com/watch?v=4_aOIA-vyBo 

—So a new universe could be born inside a black hole.

Though speculative, the idea that a black hole singularity could give rise to a universe contained in the black hole has been around for a while, and can be described mathematically.

 #Smolin, Lee (1992): “Did the universe evolve?” Class. Quantum Grav. vol. 9 173

https://www.nat.vu.nl/~wimu/Varying-Constants-Papers/Smolin-Evolve-1992.pdf   

Quote: “An alternative hypothesis, which is equivalent as far as its consequences for the subject of this paper, is that instead of an ending in a final singularity, the interior of a black hole tunnels into a new spatially compact universe”

#Frolov, V.P.;  Markov M.A., Mukhanov, V.F. (1990): “Black holes as possible sources of closed and semiclosed worlds.” Phys. Rev. D vol. 41, 383

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.41.383 

Quote: “The internal structure of spacetime inside a black hole is investigated on the assumption that

some limiting curvature exists. It is shown that the Schwarzschild metric inside the black hole can

be attached to the de Sitter one at some spacelike junction surface which may represent a short transition layer. The method of massive thin shells by Israel is used to obtain the characteristics of this

layer. It is shown that instead of the singularity the closed world can be formed inside the black

hole.” 

It has gained some traction as an alternative explanation to the horizon problem, flatness, and the structure formation problems normally explained through inflation. 

#Easson, Damien A.; Brandenberger, Robert H. (2001): “Universe Generation from Black Hole Interiors” Journal of High Energy Physics, vol, 2001

https://arxiv.org/abs/hep-th/0103019 

https://iopscience.iop.org/article/10.1088/1126-6708/2001/06/024 

Quote: “We point out that scenarios in which the universe is born from the interior of a black hole may not posses many of the problems of the Standard Big-Bang (SBB) model. In particular we demonstrate that the horizon problem, flatness, and the structure formation problem might be solved naturally, not necessarily requiring a long period of cosmological inflation. The black hole information loss problem is

also discussed. Our conclusions are completely independent of the details of general models”

—The funny thing about this scenario is that nothing has changed in the slightest outside the black hole. Watching from the outside, it still is a black sphere of nothingness. And yet, on the inside a new universe has been born.

Since the new universe is inside the black hole, outside observers will be entirely unaware of it, because the inside of the black hole can’t affect what happens outside of it (the outside of the black hole is causally disconnected from the inside).

#Smolin, Lee (1994): ”The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology”

https://arxiv.org/abs/gr-qc/9404011 

Quote: “A natural solution to the problem of the fate of black hole singularities, that has been discussed for many years , is that quantum effects cause a bounce when densities become extreme (presumably of order of the Planck density) so that the worldlines of the stars atom that have been converging begin to diverge. As there is nothing that can remove the horizon, before, at least, the evaporation time of the black hole, which is at least 1054 Hubble times for an astrophysical black hole and therefor, plausibly, beyond the scope of this paper, whatever new region of spacetime is traced by these diverging geodesics remains hidden behind the original horizon. Moreover, any observers in this new region see themselves to be in a region of spacetime which is locally indistinguishable from an expanding cosmological solution with an apparent singularity in the past of every geodesic. Thus, it would make sense to call this process the creation of a new universe that is (at least on scales shorter than 1054 Hubble times) causally disconnected from our universe .

It may then be conjectured that each black hole of our universe leads to such a creation of a new universe and that, correspondingly, the big bang in our past is the result of the formation of a black hole in another universe.”

—If the universe creates black holes that create universes, that then create new black holes that create new universes, this cosmic self-reproduction would be subject to natural selection. 

The idea of a “cosmological natural selection” was first proposed by Lee Smolin in 1992. He describes a mechanism that, under certain hypothesis (including positive curvature and a small variability between the physics of mother and daughter universes) would lead to the formation of universes with an increasingly large number of black holes, somewhat analogous to how the mechanism of biological natural selection produces populations increasingly fit to their environment. 

#Smolin, Lee (1992): “Did the universe evolve?” Class. Quantum Grav. vol. 9 173

https://www.nat.vu.nl/~wimu/Varying-Constants-Papers/Smolin-Evolve-1992.pdf 

Quote: “It is proposed that all final singularities 'bounce' or tunnel to initial singularities of new universes at which point the dimensionless parameters of the standard models of particle physics and cosmology undergo small random changes. This speculative hypothesis, plus the conventional physics of gravitational collapse, together comprise a mechanism for natural selection, in which those choices of parameters that lead to universes that produce the most black holes during their lifetime are selected for.”

—A Big Bang is a chaotic and messy event, so it’s possible that the new daughter universes would not always be fully identical to their mums. Sometimes physics may be slightly different, with some fundamental values higher or lower. 

The two main hypotheses of the “cosmological natural selection” are that universes can be born from black hole singularities and, crucially, that the universes born from black holes inherit some of the properties from their parent universes, with some small random variations. 

#Smolin, Lee (2004): “Cosmological natural selection as the explanation for the complexity of the universe” Physica A: Statistical Mechanics and its Applications, vol. 340, 4, 705-713

https://www.sciencedirect.com/science/article/abs/pii/S0378437104005801 

Quote: ”[A] theory aimed at explaining the parameters of the standard model of particle physics was introduced, which assumes the following two hypothesis about fundamental physics:

1. Black hole singularities bounce, leading to new expanding regions of spacetime, one per each black hole.

2. When this happens the dimensionless parameters of the standard model of low energy physics of the new region differ by a small random change from those in the region in which the black hole formed. Small here means with small with respect to the change that would be required to significantly change B(p), the expected number of black holes produced in the classical region of spacetime produced by the bounce. Here  p∈P , the space of dimensionless parameters of the standard model.”

—And so some universes might be able to create loads of stars, planets and black holes. Others might not, maybe creating a uniform cosmic soup where no stars, planets and black holes form. 

This sentence means to express that in some Universes, black holes will be very abundant, while in others there will be very little back holes or even no black holes. Smolin’s theory accounts for this. 

—But if all universes are born inside black holes, in the long run all universe lines that don’t create loads of black holes would die out. The universes with the conditions for loads of black holes would become the most common and spawn the most daughter universes. Survival of the fittest, but with universes instead of organisms. 

The capability of an universe to produce black holes becomes increasingly common in later generations, as universes that generate many black holes spawn many universes and pass on physics similar to their own to those universes, making the daughter universes more likely to create many black holes. 

#Smolin, Lee (1994): ”The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology”

https://arxiv.org/abs/gr-qc/9404011

Quote: “If we let P be the space of dimensionless parameters, p, then we can define an ensemble of universes by beginning with an initial value p*, and letting the system evolve through N generations. Let us define a function B(p) on P that is the expected number of future singularities generated during a lifetime of a universe with parameters p. We may observe that, for most p, B(p) is one, but there are smallregions of the parameter space where B(p) is very large. The present values of the parameters must be in one such region because there are apparently at least 1018 black holes in our universe. After N generations the ensemble then defines a probability distribution function ρN(p) on P. To give meaning to the postulate that the random steps in the parameter space are small, we may require that the mean size of the random steps in the parameter space is small compared to the width of the peaks in B(p). It then follows from elementary statistical configurations that, for any starting point p∗there is an N0 such that for all N > N0, ρN(p) is concentrated around local maxima of B(p). This is because (from the above restriction on step size) it is overwhelmingly probable that a universe picked at random from the ensemble is the progeny of a universe that had itself many black holes. But, again, because the parameters change by small

amounts at each almost-singularity this means that it is overwhelmingly probable that a universe picked at random from the ensemble itself has many black holes. Thus, we conclude that a typical universe in the ensemble (for N > N0) has parameters p close to a local maximum of B(p).”

—Our observable universe alone has created at least 1017 black holes so far. 

As established above, the observable universe contains around 1012 galaxies.

#ESA Science and Technology: Hubble (2016): “Observable Universe contains ten times more galaxies than previously thought” (retrieved 2024).

https://sci.esa.int/web/hubble/-/58444-observable-universe-contains-ten-times-more-galaxies-than-previously-thought-heic1620 

Quote: “One of the most fundamental questions in astronomy is that of just how many galaxies the Universe contains. The Hubble Deep Field images, captured in the mid-1990s, gave the first real insight into this. Myriad faint galaxies were revealed, and it was estimated that the observable Universe contains about 100 billion galaxies. Now, an international team, led by Christopher Conselice from the University of Nottingham, UK, have shown that this figure is at least ten times too low.”

The average rate of supernovae in the Milky Way, comparable with that of many other similar galaxies, is of the order 10-2 supernovae per year

#ESA (2006): “Integral identifies supernova rate for Milky Way” (retrieved 2024)

https://www.esa.int/Science_Exploration/Space_Science/Integral/Integral_identifies_supernova_rate_for_Milky_Way 

Quote: “Because astrophysicists had inferred that the likely sources are mainly massive stars, which end their lives as supernovae, they could estimate the rate of such supernova events. They obtained a rate of one supernova every 50 years - consistent with what had been indirectly found from observations of other galaxies and their comparison to the Milky Way.”

And the Universe has been around for 1010 years or so

#NASA (2024): Universe 101: “How old is the Universe?”

https://map.gsfc.nasa.gov/universe/uni_age.html 

Quote: “Measurements by the WMAP satellite can help determine the age of the universe. The detailed structure of the cosmic microwave background fluctuations depends on the current density of the universe, the composition of the universe and its expansion rate. As of 2013, WMAP determined these parameters with an accuracy of better than than 1.5%. In turn, knowing the composition with this precision, we can estimate the age of the universe to about 0.4%: 13.77 ± 0.059 billion years!”

So we have: 

1012 galaxies  × 1010 years × 10-2 supernovae per galaxy per year = 1020 supernovae

If 10% of those supernovae result in a black hole, that makes a total of 1019 supernovae.

A similar approximation is done here:

#Smolin, Lee (2004): “Cosmological natural selection as the explanation for the complexity of the universe” Physica A: Statistical Mechanics and its Applications, vol. 340, 4, 705-713

https://www.sciencedirect.com/science/article/abs/pii/S0378437104005801 

https://www.few.vu.nl/~wimu/Varying-Constants-Papers/Smolin-Physica-2004.pdf   

Quote: “There are roughly 1010 spiral galaxies in the visible universe, each has a supernova rate of roughly one per 50 years. If 10% of these leave black holes as remnants, then after 1010 years one has 1017 black holes.”

—And that would have a lovely side effect. If universes are optimized to create as many new black hole universes as possible, they are optimized to create loads of galaxies and stars. And thereby also, by accident, the conditions for life to emerge. So universes that are the best at creating new universes are also the best at creating life. If this scenario is true, who knows how many bazillions of black hole universes might be out there. All with stars and planets, potentially home to others like us. 

The conditions that lead to the development of universes with many black holes may also be the same as those leading to the development of stars and stable carbon chemistry, both important requisites for life as we know it. Hence, if a mechanism selects for universes with many black holes, it also selects for universes prone to develop an abundance of life. 

#Smolin, Lee (2004): “Cosmological natural selection as the explanation for the complexity of the universe” Physica A: Statistical Mechanics and its Applications, vol. 340, 4, 705-713,

https://www.sciencedirect.com/science/article/abs/pii/S0378437104005801 

Quote: “While most of those studying complex systems have been concerned with how, given the laws of physics, life can emerge, there turns out to be a prior issue: why are the laws of physics chosen so that complex, stable structures form? Why are there stars? Why do some burn long and stably enough to allow life to begin and evolve? Why are the atoms such as carbon and oxygen necessary for life stable and plentiful? It turns out there can only be stars and carbon chemistry if the parameters of the laws of physics take values in narrow ranges around their present values [...] The conjunction of (1) and (2) [, the main hypothesis for cosmological natural selection,] thus constitute a theory that if true would explain the values of the parameters of the standard model without recourse to the anthropic principle. This theory has been called, “cosmological natural selection”.

—So. Is our universe like this? The truth is we don’t know. While these ideas are based on real science and work on paper, they are speculative and not testable. 

Of course, to get direct proof of this theory one would have to jump inside a black hole, experience the singularity, survive with all of one’s equipment and measure the new Univere’s fundamental constants, which, on top of all the hustle, would make everyone else outside the black hole none the wiser.

However,  an indirect test has been proposed which supposedly would allow to falsify the predictions of these models.

#Smolin, Lee (2004): “Cosmological natural selection as the explanation for the complexity of the universe” Physica A: Statistical Mechanics and its Applications, vol. 340, 4, 705-713

https://www.sciencedirect.com/science/article/abs/pii/S0378437104005801  

https://www.few.vu.nl/~wimu/Varying-Constants-Papers/Smolin-Physica-2004.pdf 

Quote: “Therefore, a single observation of a neutron star whose mass M was sufficiently high would show that μ>μc, refuting Bethe and Brown’s claim for the opposite. Sufficiently high is certainly 2.5Mo, although if one is completely confident of Bethe and Brown’s upper limit of 1.5 solar masses, any value higher than this would be troubling. Furthermore, this would refute [cosmological natural selection] because it would then be the case that a decrease would lead to a world with a lower upper mass limit for neutron stars, and therefore more black holes.”

Yet this test relies on our understanding of neutron stars and their equation of state (i.e. the way matter in their interior behaves), which is still an open problem in astrophysics. Additionally, the limits of what counts as a sufficiently massive neutron star are still hazy.