## Hawking Radiation

Posted by on Wednesday, March 14, 2018

With the recent passing of legendary theoretical physicist Stephen Hawking, I have received a number of requests to explain some of his pioneering research work in a popular format. To be honest it is simply not possible to do better than Hawking's own work in communicating his research to the masses. I would strongly encourage those who are interested to read some of his many popular science books to get a true understanding of his genius.

However for those who are still reading, I will make an attempt to explain one particularly interesting piece of research, known as Hawking radiation.

Over the course of his long and illustrious career, Hawking proved a number of interesting theorems on the properties of spacetime in general and black holes in particular. His theorems on singularities in the theory of general relativity are still quoted in the academic literature on a daily basis. However the work that brought Hawking to the attention of the theoretical physics community was his proof that black holes are neither black, nor eternal.

The concept of a black hole is actually much older than most people realize. Long before Einstein had developed the theories of relativity, philosophers and scientists were already discussing the possibility that an object could be so dense that not even light could escape from its surface. Such an object would appear completely black, and would absorb everything that got near it.

Then in 1905 Einstein published the special theory of relativity, and proved that nothing can travel faster than the speed of light. Ten years later the general theory of relativity was published, adding gravitational effects, and within a year it had been discovered that there are indeed theoretical objects in the Universe that are so dense that they even trap light. These objects, dubbed black holes, are truly inescapable. Anything that goes in can never come out again. Even energy and information would be trapped until the end of time - or so we thought.

By the late 1970s physicists were starting to ask questions about the microscopic properties of black holes. For example, quantum mechanics tells us that information can never be destroyed, while general relativity tells us that anything falling into a black hole will be disappear from the Universe and leave no trace of its existence. This led to the concept that a full theory of quantum gravity would somehow add thermodynamic properties to black holes, such that entropy and information somehow exist on their surface.

And then came Stephen Hawking. He took the standard equations of quantum mechanics, but considered them in the neighbourhood of the black hole's event horizon. The same methods that theorists had been using for half a century were now adapted to regions of extreme gravity, and a truly amazing result emerged. According to the equations, subatomic particles would form near the black hole event horizon and stream out into the Universe!

As an aside, there is perhaps a more intuitive way to understand why this happens. According to the laws of quantum mechanics, empty space is never truly empty. Heisenberg's uncertainty principle tells us that there will always be little bursts of energy, which corresponds to particle-antiparticle pairs spontaneously forming at a subatomic scale, and then immediately annihilating with each other again. This is constantly happening in every part of space and at every moment in time, but because the particles disappear so quickly there is no noticeable effect. However if the particle-antiparticle pair forms near the black hole event horizon, then one of the pair can fall into the black hole before annihilation can occur, leaving its orphaned partner to become real and leave the region. In effect, a virtual particle carries negative energy into the black hole while its partner carries positive energy away from the black hole without ever having to cross the event horizon itself. And while we still do not understand how gravity works at a quantum level, it seems clear that Hawking radiation is one of the first phenomena to be predicted by the as yet unknown theory of quantum gravity.

This was a revolutionary discovery. Black holes by definition are regions of spacetime from which nothing can escape. And yet according to the laws of quantum mechanics, there would be a thermal flux of particles leaving the black hole, and the temperature would depend inversely on the surface area of the event horizon. And so a large black hole would emit a few particles, reduce its mass and surface area, and then heat up. Eventually it would become so small and hot that the black hole would instantly explode (which then creates other problems relating to the information that was once contained in the black hole, but that is a topic for another day).

Subsequent calculations using other methods confirmed this result, and the flux of particles soon become known as Hawking radiation. And if it had been detected experimentally during Hawking's lifetime it would have been been certain that the Nobel Prize would have been awarded to Hawking the same year. It is difficult to overstate how much this one discovery changed our understanding of both black holes and gravity in general.

And so that is my (perhaps oversimplified) review of Hawking radiation. And while it was Hawking's most famous academic achievement, it is truly only one of many great advances in the theory of general relativity that can be attributed to the man.

He was a great ambassador for theoretical physics, and he will be missed.

However for those who are still reading, I will make an attempt to explain one particularly interesting piece of research, known as Hawking radiation.

Over the course of his long and illustrious career, Hawking proved a number of interesting theorems on the properties of spacetime in general and black holes in particular. His theorems on singularities in the theory of general relativity are still quoted in the academic literature on a daily basis. However the work that brought Hawking to the attention of the theoretical physics community was his proof that black holes are neither black, nor eternal.

The concept of a black hole is actually much older than most people realize. Long before Einstein had developed the theories of relativity, philosophers and scientists were already discussing the possibility that an object could be so dense that not even light could escape from its surface. Such an object would appear completely black, and would absorb everything that got near it.

Then in 1905 Einstein published the special theory of relativity, and proved that nothing can travel faster than the speed of light. Ten years later the general theory of relativity was published, adding gravitational effects, and within a year it had been discovered that there are indeed theoretical objects in the Universe that are so dense that they even trap light. These objects, dubbed black holes, are truly inescapable. Anything that goes in can never come out again. Even energy and information would be trapped until the end of time - or so we thought.

By the late 1970s physicists were starting to ask questions about the microscopic properties of black holes. For example, quantum mechanics tells us that information can never be destroyed, while general relativity tells us that anything falling into a black hole will be disappear from the Universe and leave no trace of its existence. This led to the concept that a full theory of quantum gravity would somehow add thermodynamic properties to black holes, such that entropy and information somehow exist on their surface.

And then came Stephen Hawking. He took the standard equations of quantum mechanics, but considered them in the neighbourhood of the black hole's event horizon. The same methods that theorists had been using for half a century were now adapted to regions of extreme gravity, and a truly amazing result emerged. According to the equations, subatomic particles would form near the black hole event horizon and stream out into the Universe!

As an aside, there is perhaps a more intuitive way to understand why this happens. According to the laws of quantum mechanics, empty space is never truly empty. Heisenberg's uncertainty principle tells us that there will always be little bursts of energy, which corresponds to particle-antiparticle pairs spontaneously forming at a subatomic scale, and then immediately annihilating with each other again. This is constantly happening in every part of space and at every moment in time, but because the particles disappear so quickly there is no noticeable effect. However if the particle-antiparticle pair forms near the black hole event horizon, then one of the pair can fall into the black hole before annihilation can occur, leaving its orphaned partner to become real and leave the region. In effect, a virtual particle carries negative energy into the black hole while its partner carries positive energy away from the black hole without ever having to cross the event horizon itself. And while we still do not understand how gravity works at a quantum level, it seems clear that Hawking radiation is one of the first phenomena to be predicted by the as yet unknown theory of quantum gravity.

This was a revolutionary discovery. Black holes by definition are regions of spacetime from which nothing can escape. And yet according to the laws of quantum mechanics, there would be a thermal flux of particles leaving the black hole, and the temperature would depend inversely on the surface area of the event horizon. And so a large black hole would emit a few particles, reduce its mass and surface area, and then heat up. Eventually it would become so small and hot that the black hole would instantly explode (which then creates other problems relating to the information that was once contained in the black hole, but that is a topic for another day).

Subsequent calculations using other methods confirmed this result, and the flux of particles soon become known as Hawking radiation. And if it had been detected experimentally during Hawking's lifetime it would have been been certain that the Nobel Prize would have been awarded to Hawking the same year. It is difficult to overstate how much this one discovery changed our understanding of both black holes and gravity in general.

And so that is my (perhaps oversimplified) review of Hawking radiation. And while it was Hawking's most famous academic achievement, it is truly only one of many great advances in the theory of general relativity that can be attributed to the man.

He was a great ambassador for theoretical physics, and he will be missed.