The year 1915 was a revolutionary year for modern physics. It was in this year that Albert Einstein published his theory of general relativity.
Before that, for almost 200 years, people had considered gravity to be a mere attractive force between objects, as Newton had theorized. But Einstein's theory of general relativity seriously challenged that notion. According to the theory of general relativity, gravity was not just an attractive force; it was the result of a massive object bending the spacetime around it.
Albert Einstein and his field equations
To describe the interaction of gravity due to this bending effect, Einstein published ten equations, called Einstein's Field Equations. These equations provided a mathematical approach to gravity and hence, became the holy grail for astrophysicists.
But despite Einstein's equations providing a possible way to find out how gravity really works, there was one big problem. Einstein had only published the equations, not their solutions. Moreover, his equations were non-linear, and non-linear equations are difficult to solve.
Karl Schwarzschild's solution to Einstein's equations
The first person to find a solution to Einstein's equations was Karl Schwarzschild, an accomplished mathematician, theoretical physicist, and one of Einstein's colleagues. And by finding a solution to Einstein's equations, he theoretically predicted the existence of mysterious objects in the universe with infinite density and incredible gravitational attraction.
Today, we call these mysterious objects black holes and have come to accept their existence. But at the time Schwarzschild predicted the existence of black holes, most physicists disagreed. They considered black holes as mere mathematical anomalies that could not exist in reality.
After all, if a black hole could exist, then its strong gravitational field would not let anything, not even light traveling at 3x10^8 m/s, escape the black hole. So, for an observer outside the black hole watching an object falling into the black hole, the object would disappear suddenly. So, any information regarding that object (e.g., what happens to that object in the future?) would be lost to the outside world once it fell into the black hole. Hence, if a black hole existed, it would directly contradict the first law of thermodynamics, which states that energy (information) can neither be created nor be destroyed in an isolated system. That's why most people at that time did not believe that a black hole could exist.
Black holes contradict the second law of thermodynamics
Moreover, the existence of black holes would also contradict the second law of thermodynamics, which states that the entropy (a measure of disorderliness) of any isolated system will always increase. For example, according to the second law of thermodynamics, if you stop cleaning your room, it will only get dirtier with time. It will never become cleaner as time passes unless you put some effort into doing so. Thus, the entropy of an isolated system always increases with time.
All objects (matter) have entropy. So, since an object disappears when dropped into a black hole, physicists assumed that its entropy would disappear too. Therefore, the total entropy of the entire universe would go down. But according to the second law of thermodynamics, this was forbidden. Hence, black holes violated the second law of thermodynamics too.
Stephen Hawking and Jacob Bekenstein
But Stephen Hawking, the famous theoretical physicist of the 21st century, was okay with it. He thought that if black holes really didn't obey the second law of thermodynamics, then so be it. He believed that finding the truth about black holes was more important than being obsessed with the laws of physics.
But Jacob Bekenstein, a graduate student from Princeton University, did not agree with Stephen Hawking. He believed that black holes, too, must obey the second law of thermodynamics.
Jacob Bekenstein's idea
In 1970, Stephen Hawking had theorized that the event horizon (boundary) of a black hole could never get smaller. If an object fell into a black hole, the black hole absorbed it, and its event horizon got bigger. So, a black hole and its event horizon only got bigger with time and never smaller.
In 1972, Bekenstein, who had read Stephen Hawking's theory, came up with a wild idea. Every time an object fell into a black hole, the object and its entropy disappeared, while the event horizon of the black hole got bigger. So, what if the event horizon of the black hole was actually a measure of the entropy of the black hole?
Hawking was immediately flabbergasted by Bekenstein's idea. He thought that it was seriously flawed. If the entropy of the black hole were to increase, it would get hotter, and with heat comes radiation. But black holes couldn't radiate because their strong gravitational pull would never let anything escape their event horizons.
Hawking tries to prove Bekenstein wrong
So, when he returned to Cambridge, Hawking decided to prove Bekenstein wrong and started working on it. But contrary to his expectations, instead of proving Bekenstein wrong, he ended up discovering the mathematical relationship between a black hole's event horizon and its entropy and confirmed that Bekenstein's idea was indeed correct. This equation came to be known as the Bekenstein-Hawking entropy equation.
Hawking radiation
Combining Theory of General Relativity with Quantum physics
Hawking now realized that a black hole's entropy could increase with time. And when its entropy increased, the black hole would get hotter and emit radiation.
Previously, he had only considered Einstein's theory of general relativity, which told that nothing, not even radiation, could escape a black hole's gravity. But he had failed to take quantum mechanics into account, which states that pairs of particles and antiparticles appear in the universe out of empty space. One of these partners (particle/antiparticle) would have positive energy, while the other would have negative energy. So, the partner with negative energy would seek out its partner with positive energy. They would then annihilate each other and disappear within a moment.
Coming up with the idea for Hawking radiation
Hawking proposed that if such a particle-antiparticle pair were to appear near the event horizon of a black hole, it was possible for the partner with negative energy to fall into the event horizon while the other escaped, preventing them from annihilating each other. The orphaned particle (or antiparticle) with positive energy would then travel away from the event horizon of the black hole. For an observer outside the event horizon, these escaping particles would look like radiation. Today, we call this radiation Hawking radiation.
Meanwhile, due to the negative energy particle (or antiparticle) which fell into the black hole, the overall energy of the black hole would reduce. And since energy is directly proportional to mass according to Einstein (E=mc^2), the mass of the black hole would reduce too. Thus, the black hole would get smaller with time and eventually disappear.
Hawking radiation was a remarkable discovery. It completely changed the perception of people on black holes and led to the Blackhole information paradox. Yet astronomers couldn't observe Hawking radiation through a telescope. After all, astronomers can only study massive black holes with a telescope. But the more massive a black hole is, the lower its temperature, and the more insignificant the temperature of its radiation is, making it almost impossible to observe. So, Hawking never got a Nobel prize for his discovery. But his contribution to science and theoretical physics cannot be forgotten. He will always live in our memories as one of the inspirational, brilliant theoretical physicists of the 21st century.
