Black Holes Are Not Totally Black: The Hawking's Legacy

The thought of what if we hide a cup of tea inside a black hole led to the prediction of the black hole emission!

Can a star have such a strong gravitational pull that even light cannot escape from it? In the 18th century, John Michell and Pierre-Simon Laplace delved into this profound question. Today, we refer to these fascinating objects as black holes in astrophysics. 

While the notion of such celestial objects appeared several times in the literature in the first half of the last century, the concept of black holes was so outlandish that it took decades of speculation, debate, rigorous research, and astronomical observations before it was widely acknowledged and embraced to its current popularity.

Just a year after Albert Einstein formulated gravity as the theory of spacetime and derived his groundbreaking field equations in 1915, Karl Schwarzschild worked out an elegant solution to the complex equations for spherically symmetric astrophysical objects. This solution revealed two intriguing aspects—the singularity and the event horizon—that define black holes.

Singularity represents the central region, and the event horizon marks the surface of no return through which anything can pass inside, but nothing can escape, even the light. The appearance of these horizons requires an enormous mass to be concentrated in a tiny region.

For example, if all of the mass of the earth is squeezed into the size of a peanut, an event horizon will show up. Compressing the sun's mass within a 3 km radius would lead to an event horizon popping up. While such objects were mathematically conceivable, their formation in nature was unthinkable. Even Einstein was sceptical about the extreme predictions that his equations revealed. 

Some clarity emerged from studies focusing on dying stars. The stars in our night sky are glowing gas balls that have existed in a state of balance for millions of years, the combination of radiation and gas pressure holding against the gravitational force. The radiation pressure is sustained as long as the nuclear fuel inside burns, in simplest terms, till all hydrogen has been converted to helium. When stars reach this stage, they shed their outer layers, contract immensely, and transform into remarkably compact stars like white dwarfs and neutron stars.

During that period, astronomers had already observed several white dwarfs. They had masses similar to that of the sun but were significantly smaller. However, not to the extent that singularities and horizons could emerge.

Subrahmanyan Chandrasekhar's work in the 1930s demonstrated that stars in their final stages, transforming into white dwarfs, remain stable only up to a critical limit of 1.4 solar masses. In parallel, Lev Landau also contributed by showing that stars ending their life as neutron stars (neutron-filled stars) also have a maximum mass limit for stability. 

The groundbreaking work of Robert Oppenheimer and Hartland Snyder in 1939, titled "On Continued Gravitational Contraction", offered crucial insights into what could happen to stars beyond these mass limits. They showed that when a star's outward pressure is no longer enough to resist gravity, these so-called zero-pressure stars will eventually collapse to a singularity, a point of extreme density surrounded by an event horizon—ultimately giving rise to a black hole.

However, these findings were met with scepticism as the assumption of the spherically symmetric collapse considered was far from the realistic collapses, which could be asymmetric. In addition, it also lacked other astrophysical complexities. As a result, within the scientific community, the notion persisted that nature would somehow intervene to stop such a catastrophic contraction of stars.

Things began to take a turn during the golden age of general relativity, which began in the 1960s. Scientific focus remarkably shifted towards black holes and related topics. Researchers like Royy Kerr and Ezra Newmann developed analytical solutions for rotating and charged black holes. 

In 1967, John Wheeler coined the term "black holes," which has persisted in the field ever since. Two years later, in his 1969 paper, Roger Penrose passionately advocated for black holes and stated, "I only wish to make a plea for black holes to be taken seriously and their consequences to be explored in full detail".

Using the solid mathematical framework, Penrose also demonstrated that the formation of black holes is inevitable, and the process of collapse will not halt. For which he was awarded the Nobel Prize in 2020. His contributions established a strong groundwork for subsequent research and advancements in black hole physics. 

Around the same period, Quasar sightings, such as 3C273, emerged. It seemed unlikely that these far-off and luminous objects derived their energy from nuclear reactions. Instead, all indications pointed to the possibility that they were powered by gravitational energy generated during the collapse. This provided credibility to the theory of the Oppenheimer-Snyder collapse.

Furthermore, in the 1970s, the discovery of Cygnus-X1, an X-ray-emitting source within our galaxy, spurred speculation that it was a black hole. This speculation eventually turned into the first concrete proof of black holes.

A fascinating black hole theory, the no-hair theorem, was also put forward during this period. It states that practically all properties and details about black holes vanish behind the event horizon during their formation, invisible to outside observers. The black hole's only characteristics are its mass, angular momentum, and charge. In contrast, for typical stars, we can attribute numerous fundamental/independent quantities to them, not just these three. Hence, the phrase no-hair theorem for the black holes. 

With these, black holes emerged as systems wherein anything could enter and disappear, but nothing could escape. A system characterized by only three basic properties. However, this notion of a black hole contradicted a well-established law of physics.

A conversation between physicist John Archibald Wheeler and graduate student Jacob Bekenstein at Princeton, discussing hiding tea cups in a black hole, led to a profound revelation.  A cosmic rule, the second law of thermodynamics, was at the heart of this discussion. According to this law, an isolated system's entropy, chaos, or disorder should increase with time.

For instance, when a hot object interacts with a cold one, the heat energy disperses, increasing chaos or disorder within the system. Moreover, this principle also applies to our expanding Universe—a closed system. For which disorder or entropy increases as time advances.

Wheeler's suggestion was intriguing: he proposed that concealing hot tea cups within a black hole would result in their disappearance, along with their associated entropy for an external observer. As a consequence, the entropy of the Universe would decrease by a certain amount, in contrast to the second law of thermodynamics. Wheeler further proposed that this disappearance of entropy inside the black hole potentially allows us to evade the second law of thermodynamics. 

After extensive contemplation, Bekenstein asserted that, in hiding the cup of tea, the entropy of the black hole itself would increase. Bekenstein's idea introduced the revolutionary notion that black holes, beyond their fundamental properties like mass, spin, and charge, also possessed entropy. This marked a pivotal moment in astrophysics, as it assigned a thermodynamic property to black holes.

Bekenstein also linked this entropy to the event horizon of a black hole. This was motivated by the idea that when an object, like a teacup, goes into a black hole, there is a simultaneous increase in the mass and the area of the event horizon of the black hole.

In works that followed, several parallels appeared between a thermally hot object and a black hole. In a state of equilibrium, an object maintains a constant temperature across its surface. Similarly, black holes exhibit a constant surface gravity over the horizon. This led to the proposal that temperature and surface gravity are connected. 

When different hot substances from diverse containers are mixed, the combined system's entropy exceeds the sum of the entropy of each container. A similar principle applies when two black holes collide and merge. The resulting new black hole indicated a horizon area greater than the sum of the horizon areas of the colliding black holes. This led to the proposal that the entropy of a black hole is closely linked to the horizon area.

In their landmark work published in 1973, James Bardeen, Brandon Carter, and Stephen Hawking developed the four laws of black hole mechanics with mathematical rigour, drawing an analogy with the three laws of thermodynamics and the zeroth law. Still, it was very tricky for physicists to figure out what temperature and entropy meant in the context of black holes. At first, it was thought parallels with surface gravity and the horizon were just analogies, not actual links. 

During the same year, Bekenstein formulated an equation linking the temperature of a black hole and its surface gravity and asserted that black holes inherently possess a finite temperature. Although a typical object with a finite temperature is expected to give off radiation, the uniqueness of a black hole is its ability to prevent anything, even light, from escaping. Hence, according to classical physics, black holes ought to be black, and the gravitational force of a black hole would prevent the release of any form of radiation. 

Eventually, Hawking's exploration of quantum effects in the black hole background yielded a breakthrough revelation: black holes emit radiation. In his 1974 work, he writes, "Bekenstein suggested on thermodynamic grounds that some multiple of surface gravity (K) should be regarded as the temperature of a black hole. He did not, however, suggest that a black hole could emit particles as well as absorb them. For this reason, Bardeen, Carter and I considered that the thermodynamical similarity between surface gravity and temperature was only an analogy. The present result seems to indicate, however, that there may be more to it than this''.

His original research focused on the classical spacetime of Schwarzschild black holes and the behaviour of the vacuum quantum field in this gravitational setting. 

Quantum physics states that space that prevails everywhere around us is not as empty. Vacuum fluctuations occur everywhere in space. Particle-antiparticle pairs emerge momentarily from the void, get annihilated, and then disappear again. This could be an electron-positron pair, proton-antiproton pair, photon-photon or others. These particles are virtual and are not real particles. They pop out of nothing, violating energy conservation, and ought to vanish for this very reason. However, due to the presence of strong electric fields or gravitational fields, these particles can acquire energy from the field and become real particles. 

Hawking showed that the vacuum fluctuations occurring near the vicinity of black holes are affected by the event horizon and curvature of the spacetime. This influence leads to the creation of particles (real ones), with the necessary energy sourced from the black hole's mass-energy. Consequently, these newly formed particles are emitted from the vicinity of the black hole, giving rise to what is now known as Hawking radiation. Primarily, these emissions are photons, although the emission of other particle pairs is also theoretically possible, such as neutrino-antineutrinos and protons-antiprotons, etc. However, creating these massive particle pairs requires a significant amount of energy, equivalent to E=mc2. 

Hawking radiation is inversely proportional to the mass of the black hole and is a highly faint emission. To illustrate, a ten solar mass black hole exhibits a Hawking temperature of approximately 10-9 Kelvin, and the associated luminosity is 10-31 Watts. A lot less than what stars and other celestial objects normally give off. Hence, detecting these emissions lies beyond the current observational capabilities.

These insignificant emissions, however, result in the gradual mass loss of black holes, causing them to shrink over time, and eventually, the black holes evaporate in a final cataclysmic event. For ten solar mass black holes, the time for evaporation is about 1070 years, significantly exceeding the present age of our Universe, which is 13.8 billion years. Hence, it is improbable that any typical black hole would experience the evaporation fate in the present or near future.

However, tiny primordial black holes formed from the collapse of dense regions during the early Universe might allow us to get a glimpse of the evaporation phenomenon. Unlike typical black holes that form when stars die off, these primordial black holes can have sub-solar masses. Their masses could be as small as that of planets or asteroids or even much lesser, allowing for their potential evaporation within the Universe's lifespan. As a result, these black holes stand out as the sole sources for observational validation of Hawking's predictions. And a way to establish that black holes are indeed not black.

The investigation of black holes within our Universe remains a continuous endeavour, with many aspects of them still awaiting discovery. Alongside theoretical research, computer simulations and observations using electromagnetic telescopes and gravitational wave detectors contribute to this quest. As we contemplate the perplexing and captivating enigmas of black holes, Hawking's profound words resonate: "It is said that fact is sometimes stranger than fiction, and nowhere is this more true than in the case of black holes. Black holes are stranger than anything dreamt up by science fiction writers, but they are firmly matters of science fact".