Kurzgesagt – In a Nutshell
Sources – Black Holes
We would like to thank Prof. Matthew Caplan (Illinois State University) for his great help with this script.
– Space and time are the grand stage where the play of the universe unfolds. But space isn’t a fixed stage and time doesn’t tick the same for everyone everywhere. In short, they are relative.
The link below is to an MIT lecture introducing special relativity. It is clearly explained, and makes evident why we know that time does not flow the same way everywhere in the universe, even though thinking about it might make your head hurt!
#Spacetime: Introduction to Special Relativity, Scott Hughes, 2005
http://web.mit.edu/sahughes/www/8.022/lec11.pdf
Quote. “These postulates [the speed of light and laws of physics are the same everywhere] have consequences that are rather amazing. In particular, it means that inertial observers in different frames of reference measure different intervals of time between events, and different spatial separations between events. As we’ll see in a moment, clocks that appear to be moving run slow; rulers that appear to be moving are shrunk.”
– Matter bends space and bent space tells matter how to move. Put some stars and planets on the stage, and it sags underneath them. That misshapen stage, with all its little warps and dips, gives us gravity.
#Spacetime Curvature, ESA, 2015
https://sci.esa.int/web/lisa-pathfinder/-/56434-spacetime-curvature
Quote. “According to Albert Einstein's general theory of relativity, gravity is no longer a force that acts on massive bodies, as viewed by Isaac Newton's universal gravitation. Instead, general relativity links gravity to the geometry of spacetime itself, and particularly to its curvature.”
Quote. “In general relativity, spacetime is not 'flat' but is curved by the presence of massive bodies.”
– Black holes do not just bend the stage, they are like trap doors. Places with so much mass that the universe formed a ‘no-go’ zone where the rules change. Most black holes form when very massive stars die.
#What Is a Black Hole?, NASA, 2014
https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-black-hole-58.html
Quote. “The most common type of medium-sized black holes is called "stellar." The mass of a stellar black hole can be up to 20 times greater than the mass of the sun and can fit inside a ball with a diameter of about 10 miles. Dozens of stellar mass black holes may exist within the Milky Way galaxy.”
– We explained this process in detail in our neutron star video – all you need to know, that in the final moments of really massive stars, their insides implode, at nearly a quarter of the speed of light.
The collapse of matter into a star’s core can reach 70,000 km/s, which is 23% of the speed of light.
#Gravitational Waves from Gravitational Collapse, Kimberly C. B. New, 2003
https://www.researchgate.net/publication/26386593_Gravitational_Waves_from_Gravitational_Collapse
Quote. “Approximately 70% of the inner portion of the core collapses homologously and subsonically. The outer core collapses at supersonic speeds. The maximum velocity of the outer regions of the core reaches ∼ 7 × 10^4 km s−1. It takes just 1 s for an earth–sized core to collapse to a radius of 50 km”
If you haven’t watched our previous video on Neutron Stars, here it is:
Neutron Stars – The Most Extreme Things that are not Black Holes, Kurzgesagt, 2019
– This packs so much mass, so close together that it creates something so dense that it sort of breaks the stage of the universe. A black hole with ten times the mass of the sun would be barely 60 kilometers across.
If we apply the equation for the radius of a black to an object of 10 solar masses (M=2 * 10^31 kg), we obtain a value of 29,644 m. That is a diameter of 59,288 m or about 60 km.
#Schwarzschild Radius, Cosmos, retrieved 2020
https://astronomy.swin.edu.au/cosmos/S/Schwarzschild+Radius
Quote. “The Schwarzschild radius is the radius of the event horizon surrounding a non-rotating black hole. Any object with a physical radius smaller than its Schwarzschild radius will be a black hole. This quantity was first derived by Karl Schwarzschild in 1916:
Rs = 2GM/c^2”
You can work out the size and other properties of black holes using the handy online calculator below.
#Black Hole Parameters, Ian Mallett, retrieved 2020
– If you look directly at a black hole it looks like... nothing. The space under their control is blocked by an invisible, one-way border called the event horizon. The event horizon forms a shell around a region of space that, once entered, is shielded from the rest of the universe forever. Because the black hole trap door deforms space so much, not even light can escape it. And with nothing escaping to transfer information from the inside, it’s impossible to tell what it really looks like.
#Cross section of a black hole, Johan Jarnestad, retrieved 2020.
https://www.nobelprize.org/uploads/2020/10/fig2-phy-en-cross-section.pdf
Quote. “When a massive star collapses under its own gravity, it forms a black hole that is so heavy that it captures everything that passes its event horizon. Not even light can escape. At the event horizon, time replaces space and points only forward. The flow of time carries everything towards a singularity furthest inside the black hole, where density is infinite and time ends.”
There is a long history of scientists wondering about what happens to the information about particles after it enters a black hole. Some thought it would just get trapped forever. Stephen Hawking’s theory that black holes eventually evaporate made things worse, as he implied that information entering a black hole would eventually be destroyed.
#Information Loss in Black Holes, Stephen Hawking, 2005
https://arxiv.org/pdf/hep-th/0507171.pdf
Quote. “[The] theorem implied that all information about the collapsing body was lost from the outside region apart from three conserved quantities: the mass, the angular momentum, and the electric charge. This loss of information wasn’t a problem in the classical theory. A classical black hole would last forever and the information could be thought of as preserved inside it, but just not very accessible. However, the situation changed when I discovered that quantum effects would cause a black hole to radiate at a steady rate At least in the approximation I was using the radiation from the black hole would be completely thermal and would carry no information. So what would happen to all that information locked inside a black hole that evaporated away and disappeared completely?”
– We still can observe black holes because of their effect on matter. Things can orbit black holes just as they can orbit the sun or a planet.
From far away, it would feel the same to orbit our Sun or a black hole of 1 solar mass, because they have the same gravitational effect.
#Black Holes, Wallace H Tucker, retrieved 2020
https://history.nasa.gov/SP-466/ch17.htm
Quote. “If we were to send a probe toward an isolated black hole, the probe would detect no radiation from the black hole. It would, however, sense a gravitational field, because the black hole has mass. As long as the probe were a safe distance away, say a few million kilometers, the gravitational field it sensed would be no different from the gravitational field produced by a normal star of the same mass. The only difference would be that no star would be visible, even though the probe could sense the presence of a large concentration of matter through the gravitational forces. At this point the probe could still escape from the gravitational pull of the black hole, if we could give it a boost of energy from a rocket, for example.”
In addition to the gravitational effect they have on surrounding matter, black holes are detectable in other ways. They are themselves invisible, but they can be surrounded by swirling matter hot enough to emit X-rays. These X-rays can be picked up by observatories like Chandra.
#Chandra X-ray Observatory Center, Harvard, 1999
https://chandra.harvard.edu/graphics/press/fact4-print.pdf
Quote. “Some of the most intense X-ray sources in the universe are caused by super-hot gas that is swirling toward a black hole. As the tremendous gravity of a black hole pulls gas and dust particles toward it, the particles speed up and form a rapidly rotating flattened disk. Friction caused by collisions between the particles heats them to extreme temperatures. Just before they pass beyond the event horizon of the black hole, the particles produce X-rays as their temperatures rise to many millions of degrees. By precisely determining the energy of individual X-rays, the Chandra X-ray Observatory can measure the motion of particles near black holes.”
– Many black holes have discs of matter orbiting outside the event horizon. This matter can become incredibly hot as close orbits can speed this matter up to half the speed of light, and tiny amounts of friction and collisions between particles heat them to a billion degrees, making the space around these black holes, ironically, incredibly bright.
#Accretion Disk Spectra from Black Hole X-ray Binaries, Kristina Salgado, 2015
https://scholar.colorado.edu/downloads/j67314292
Quote. “As the gas in the accretion disk orbits faster and faster as it approaches the black hole, the gas heats up to temperatures exceeding 10 million degrees Kelvin. Therefore, the accretion disk glows as X-ray light and this radiation coming from the inner regions of the disk is what astronomers observe with space-borne X-ray telescopes.”
Accretion disks actually produce a range of temperatures, from a few thousand to a few billion Kelvin.
#In the light of black holes - Accretion discs, coronae and jets around accreting black holes, Julien Malzac, 2008
https://tel.archives-ouvertes.fr/tel-00332415/document
Quote. “ A black hole may accrete gas from its environment (or from a companion star in the case of stellar black holes) and then radiate a fraction of the gravitational energy of the infalling material. Due to viscosity (and other dissipation processes) the infalling gas can be heated up to a very high temperature. The observations indicate the presence of a very hot plasma with a temperature of a few billion Kelvin in the inner parts of the accretion flow leading to copious X-ray and γ-ray emission.”
– If you hovered just outside the event horizon, at the photon sphere, in any direction you’d just see… yourself! Straight ahead would be the back of your own head, as light from your back travels around the black hole to your eyes.
#Virtual Trips to Black Holes and Neutron Stars, Robert Nemiroff, retrieved 2020
https://apod.nasa.gov/htmltest/gifcity/gotops.html
Quote. “A photon sphere is a location where gravity is so strong that light can travel in circles. Photons orbit the black hole at the distance of the photon sphere. A photon could leave the back of your head, go once around the black hole, and be seen by your eye - you can see the back of your head.”
– Gravity also alters the passage of time itself. The stronger the gravity, the slower time passes. While you watch the universe above you speed up, those far away will watch you in slow motion. If you chose to fly away from the black hole, you might find that eons have passed for the rest of the universe, a freakish one-way time-travel trip to the future where your loved ones are long dead.
At the event horizon of a black hole, time under the influence of gravity becomes so distorted that an infinite amount of time will appear to pass outside for each second spent inside that location.
#What Does a Black Hole Look Like?, Charles D. Bailyn, 2014
http://assets.press.princeton.edu/chapters/s10292.pdf
Quote. “There are thus a number of situations related to black holes in which physical quantities should become infinite. At r = Rs , terms of the metric become infinite, and time stops. At the center of the black hole, where r = 0, the density of matter becomes infinite.”
– But getting close to a black hole can be incredibly dangerous. A painful death by ‘spaghettification’ awaits you. Because your feet are closer to the black hole than your head they feel a stronger pull of gravity, enough to pull you apart. As you descend it gets worse, the pulling gets stronger, your body squeezed thinner and straighter until you’ve been reduced to a thin stream of hot plasma, gobbled up in one final slurp, never to be seen again.
#Introduction to black hole astrophysics, Gustavo E. Romero, 2010
http://astrofrelat.fcaglp.unlp.edu.ar/agujeros_negros/media/Romero-Apunte_agujeros_negros.pdf
Quote. “The tidal acceleration on a body of finite size Δr is simply (2rg/r^3)c^2 Δr. This acceleration and the corresponding force becomes infinite at the singularity. As the object falls into the black hole, tidal forces act to tear it apart. This painful process is known as “spaghettification”. The process can be significant long before crossing the event horizon, depending on the mass of the black hole”
– Spaghettification is only a risk with smaller black holes, since they have much smaller radii. If you go to the center of a galaxy and find a supermassive black hole, you might be able to experience crossing the event horizon.
The gravitational gradients around a supermassive black hole are so mild that you could cross the event horizon unharmed.
#General Relativity: An Introduction for Physicists, M. P. Hobson et al., 2006
https://books.google.co.uk/books?id=5dryXCWR7EIC&pg=PA265&redir_esc=y#v=onepage&q&f=false
Quote:
– Here, inside the event horizon, space and time are so horribly broken that real time travel is possible, so it’s probably a good thing that nothing gets out. If anything could escape it could create all sorts of time travel paradoxes and issues that break the universe. As scary as the event horizon is, it keeps us safe from that drama.
At the heart of a black hole is what we imagine to be a single point, or singularity, where all the mass is concentrated. Calculations using classical physics give us nonsensical answers; when we divide mass by zero volume, we get infinite density. Infinite density means infinite gravity, which would in turn mean that time is stretched so much that it hasn’t moved since the black hole was formed. Clearly, classical physics is insufficient to describe or predict the behaviour of singularities. Different physics models (like quantum mechanics or string theory) are needed to make sense of them.
#Singularities and Black Holes, Erik Curiel, 2019
https://plato.stanford.edu/entries/spacetime-singularities/
Quote. “A spacetime singularity is a breakdown in spacetime, either in its geometry or in some other basic physical structure. It is a topic of ongoing physical and philosophical research to clarify both the nature and significance of such pathologies. When it is the fundamental geometry that breaks down, spacetime singularities are often viewed as an end, or “edge”, of spacetime itself.”
Even quantum mechanics can only give way to speculation and supposition when it comes to what happens behind a black hole’s event horizon. Our understanding of these mysterious cosmic entities remains incomplete.
#Space-time Disintegration beyond Event Horizon and its Consequences, Pranav Sharma, 2015
Quote. “Beyond event horizon disintegration will take place where spacetime will change its nature sharply with respect to the changing forces inside a black hole. The space will start disintegrating towards absolute minimum drawing sharply down.
Whenever such space-time disintegration is taking place, an interacting particle should play mediation between quantum spacetime entities. To model this we can say that space-time is made up of quantum values bound together by an interacting particle. Whenever there is a move up in the space-time ladder or move down a particle (say J) should be consumed or released respectively.”
– In the center of the black hole, we find the singularity. A single point with all the matter that has ever crossed the event horizon, all crushed to a point infinitely small. There is no memory of the things that made it as stuff disappears down the black hole trapdoor forever. The singularity makes all things equal. This actually breaks the universe in really cool ways. We made a whole video about this problem if you want to learn more. But in a nutshell, everything that comes too close becomes black hole matter, concentrated at the singularity.
#Black hole, Encyclopaedia Britannica, 2020
https://www.britannica.com/science/black-hole#ref190750
Quote: “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.”
If you haven’t watched a previous video on how weird Black Holes can get, have this:
Why Black Holes Could Delete The Universe – The Information Paradox, 2017
– This lack of a memory of its past, means that a black hole has only three properties: their mass, spin, and electric charge. Everything else is lost. They’re a lot like fundamental particles in that respect. This actually means that every single black hole in the universe is the same. Sure, their mass is different and some spin faster than others. But If we were to put all the singularities into a magical physics museum, they would be identical, like electrons.
Black holes absorb matter into a smooth, featureless singularity with only basic properties - which can be funnily described as a ‘hairless’ object. All other information is trapped behind the event horizon. Hawking’s theory on evaporating black holes goes a step further, suggesting that information is eventually destroyed.
#Classical and Quantum Approaches to Black Holes, Ovidiu Cristinel Stoica, 2018
https://www.hindawi.com/journals/ahep/2018/4130417/
Quote. “By applying general relativity and quantum field theory on curved spacetime, Hawking arrives at the conclusion that the information is lost in the black holes, and this breaks the predictability. Apparently, no matter how was formed and what information was contained in the matter falling in a black hole, the only degrees of freedom characterizing it are its mass, angular momentum, and electric charge, so black holes are “hairless”. This means that the information describing the matter crossing the event horizon is lost, because nothing outside the black hole reminds us of it. In general relativity, this information loss is irreversible”
– Also, basically everything you’ve ever heard about black holes, even in this video, is about theoretical black holes that aren’t spinning, because their math is so much easier. But since black holes were born from dying stars that were spinning extremely quickly in their last moments, as far as we know, all black holes in the universe should be spinning right now. At incredible speeds too, up to 90 % the speed of light. This means in reality, black holes are even more screwed up than they usually get credit for.
We’ve directly observed a black hole spinning at half the speed of light, while data suggests there are black holes elsewhere spinning at 90% of the speed of light. In fact, the majority of black holes seem to be spinning at high fractions of the speed of light.
#Observing Black Holes Spin, Christopher S. Reynolds, 2019
https://arxiv.org/pdf/1903.11704.pdf
Quote. “we find that below about 30 million solar masses, the vast majority of SMBHs examined seem to be rapidly spinning (a∼> 0.9). For more massive black holes, however, we appear to pick up a population of more slowly spinning objects (a ∼ 0.5 − 0.7).”
– The singularities of rotating black holes are even wilder. The rotation causes them to swell outwards into a sort of ringularity. This rotation is so powerful, that space itself is dragged along. This creates another region around spinning black holes, called the Ergosphere where it’s impossible to stay still, no matter how hard you try. Like a rushing whirlpool of spacetime, the tide is irresistible and black hole makes you orbit it whether you want to or not.
New Zealand mathematician Roy Kerr, one of the major contributors to black hole theory, built on earlier work by German physicist Karl Schwarzschild to describe the form of the event horizon around a rotating black hole. He suggested that instead of a sphere with a certain radius around a point-like singularity, it would spread into a ring around a flat disk-like singularity.
#The Schwarzschild Solution and Black Holes, Sean M. Carroll, 1997
https://preposterousuniverse.com/wp-content/uploads/grnotes-seven.pdf
Quote. “This seems like a funny result, but remember that r = 0 is not a point in space, but a disk; the set of points r = 0, θ = π/2 is actually the ring at the edge of this disk. The rotation has “softened” the Schwarzschild singularity, spreading it out over a ring”
The gravitational influence of a rotating black hole spreads into an ‘ergosphere’. It is a flattened ellipsoid that is widest at the equator and touching the black hole’s event horizon at the poles.
#Physics 161: Black Holes, Kim Griest, 2010
https://courses.physics.ucsd.edu/2010/Winter/physics161/p161.26feb10.pdf
Quote. “The region inside this ellipsoid is called the ergosphere. Inside this region nothing can stand still. Everything rotates with the hole. The spinning hole actually drags the spacetime around it with it! Light itself going against the rotation direction will be carried backward around the hole. This is called “frame dragging”. If you drop something straight down into a spinning black hole, it will start orbiting the hole even though there is nothing but empty space outside the hole.”
You can find below a diagram of the different surfaces and parts of a rotating black hole. Note how the singularity is a ring and the ergosphere stretches well beyond the event horizon.
#Rotating Black Holes, Muhammad Firdaus Mohd Soberi, 2015
http://faculty.washington.edu/goussiou/486_W15/Soberi_BlackHole.pdf
– Ok. So what will happen with black holes as the universe ages and dies around them? Again, we don’t know but have some ideas based on our current understanding of physics: Hawking radiation. In quantum field theory the vacuum of space is boiling with quantum fluctuations. These fluctuations are creating matter and antimatter pairs of particles from nothing which only exist for a very short time before annihilating. When this happens near the event horizon of a black hole, one of these particles can fall in, stopping them from annihilating. The escaping particle is Hawking radiation. Ultimately, the mass of this particle must come from the black hole, so over eons black holes will shrink and radiate away. Hawking radiation is not the stuff that fell into the black hole, it’s new stuff, stealing mass from it. As the black hole shrinks the Hawking radiation gets stronger, faster and faster, until what’s left eventually evaporates in a flash of high energy radiation like a nuclear bomb. And then, nothing.
There is no-one better placed to explain what Hawking radiation is than Stephen Hawking himself. His 1974 and 1975 papers show how this theory is the direct result of applying quantum mechanics to the more classical understanding of black holes.
#Particle Creation by Black Holes, Stephen W. Hawking, 1975
https://www.brainmaster.com/software/pubs/physics/Hawking%20Particle%20Creation.pdf
Quote. “In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature [determined by] the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 10^15g would have evaporated by now.”
#Black hole explosions?, Stephen W. Hawking, 1974
https://www.nature.com/articles/248030a0
Quote. “Near the end of its life the rate of emission would be very high and about 10^80 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs”
– But that won’t happen for a long long time. A black hole with the mass of our sun has a lifetime of 10^67 years. Which means that it would take 10,000 billion, billion, billion, billion,billion, billion years, to lose 0.0000001% of its mass.
#Black Hole Math, NASA, 2019
https://www.nasa.gov/sites/default/files/atoms/files/black_hole_math.pdf
Quote. “The formula for the evaporation time of a black hole with a mass of M in kilograms is given by t=10256 * π^2 * G^2 * M^3 / ( h * c^4)”
These are the appropriate values:
Pi or π=3.142
The gravitational constant G= 6.67 * 10^-11
The Planck constant h=6.628 * 10^-34
The speed of light c=3 * 10^8
If we input the mass M as 1.99 * 10^30 kg, which is one solar mass, we obtain a time value t equal to 6.7 *10^74 seconds or 2.1 * 10^67 years.
– But most black holes are way more massive than our sun. The most massive supermassive black holes in the centers of galaxies have lifetimes of 10^100 years.
#A New Kind of Black Hole, NASA, retrieved 2020
https://www.nasa.gov/vision/universe/starsgalaxies/Black_Hole.html
Quote. “Supermassive black holes exist in the center of most galaxies, including our own Milky Way Galaxy. They are astonishingly heavy, with masses ranging from millions to billions of solar masses. Why they are so incredibly massive isn't known, but astronomers are pretty sure their development is linked to their presence at the center of their galaxy. There are so many stars and so much gas and dust that the black hole can grow large very quickly. And since many galaxies collide repeatedly during their long lifetimes, supermassive black holes have a ready-made way to collide and coalesce into even heavier supermassive black holes.”
The largest black hole in the list below is TON 618, with a mass listed as log(M/Mo)=10.8. That means that the mass of this black hole is 10^10.8 times higher than the mass of our Sun, which is the equivalent to 63 billion solar masses or 1.25* 10^41 kg. We can input this figure into the previous ‘black hole evaporation time’ formula to obtain a value of 1.63 * 10^107 seconds. That is equivalent to 0.52 * 10^100 years. For comparison, the Universe has existed for 1.38 * 10^10 years.
#A list of 101 Supermassive Black Holes, Sara Nóbrega and José Laurindo de Góis Nóbrega Sobrinho, 2020
https://www.researchgate.net/publication/339329648_A_list_of_101_Supermassive_Black_Holes
– How long is that? Imagine an hourglass, filled with one grain of sand for every single particle in the universe. Every ten billion years one single grain of sand falls to the bottom. If we waited for the entire sand to fall down, not even a percent of the lifetimes of these black holes would have passed. There is no good concept for our brains to grasp these time scales.
Ten billion years is 10^10 years. 6 * 10^79 grains of sand times 10^10 years gives us ‘only’ 6 * 10^89 years, which is less than 0.000000001% of the 10^100 figure we mentioned above.
#Mass, Size, and Density of the Universe, National Solar Observatory, retrieved 2020
https://people.cs.umass.edu/~immerman/stanford/universe.html
Quote. “If the Universe is at the critical density, then the total mass of the Universe is closer to 1e53 kg, and the number of atoms (assuming that most of the mass is in the form of hydrogen atoms) about 6e79”