Hawking Radiation

Black holes are regions of space with such a strong gravitational field that nothing, even light, can’t escape. They were a theoretical construct from the theory of general relativity, and only observed in April 2019. In the 1970s, questions arose if black holes had entropy and a temperature. The results of Bekenstein, Starobinsky, Hawking and Zeldovich showed a beautiful connection between quantum mechanics and general relativity and completely changed our understanding of black holes. Let’s examine what Hawking radiation is.

The equation for the temperature of a black hole on Hawking’s grave. Credit: Westminster Abbey.

When matter falls into a black hole, it cannot go back out into the universe, which should break the second law of thermodynamics. This law states that entropy, or the measure of disorder, should always increase. It makes intuitive sense, the longer you live in your apartment without cleaning it, the messier it will become. A black hole is kind of like throwing your messy clothes and dirty dishes outside the window, increasing order and decreasing entropy.

In 1972, a Princeton student Jacob Bekenstein, showed that this paradox could be solved if the event horizon increased when matter was consumed. At the same time on the other side of the Atlantic ocean, Hawking began doubting Bekenstein’s solution. Entropy is strongly connected with thermal energy, so this expansion of the event horizon would also mean that a black hole had to emit radiation.

To find out more, Hawking visited Starobinsky and Zeldovich who were simultanously working at this same problem. They convinced him that rotating black holes could emit radiation. Hawking attempted to disprove Bekenstein, but at the same time showed that rotating and non-rotating black holes do emit radiation. This was different from the regular black-body radiation that every object emits, but it still meant that black holes were losing mass.

Here comes the beautiful part. This radiation is due to pairs of virtual particles appearing at the event horizon. These are a particle and an antiparticle pairs, which arise due to fluctuations in the quantum field. Normally, they would be annihilated soon after their creation, nonetheless sometimes a black hole consumes one of the particles and the other flies off into space. This causes the black hole to lose the mass equivalent to that one particle. It is a complicated process governed by loads of equations so read about it here in more detail.

A diagram of Hawking radiation. Credit: Areeba Merriam.

This radiation happens at a tremendously slow rate, relative to the size of the black hole. For many of them, the time taken to disappear due to Hawking radiation is orders of magnitude higher than the remaining lifespan of the universe. The time taken is proportional to mass cubed. For a black hole with the mass equivalent to the mass of our sun, which is tiny in black hole terms, the time taken is already greater than the lifespan of the universe.

The formula for the time taken for a black hole to evaporate, where M is the mass of the black hole and M dot is the mass of our sun.

Unfortunately, this radiation is too faint to be observed experimentally with current technology. There have been attempts to simulate this radiation with a white hole event horizon, yet the experimental results were not replicated and the conclusions remain inconclusive.

If you want to learn more, I strongly recommend reading the chapter Black Holes Ain’t So Black from A Brief History of Time by Stephen Hawking. It’s a fantastic explanation with a lot of diagrams from one of the people who discovered it. Also, check out this video from PBS SpaceTime.


Merriam, A. (n.d.). Hawking Radiation of Relativistic Particles from the Horizon of Black Holes. Medium. https://www.cantorsparadise.com/hawking-radiation-of-relativistic-particles-from-the-horizon-of-black-holes-741c9f7b230d

S.A. (n.d.). What Is Hawking Radiation? ScienceAlert. https://www.sciencealert.com/hawking-radiation

Spindel, R. (2011). Hawking radiation. Scholarpedia, 6(12), 6958. https://doi.org/10.4249/scholarpedia.6958

Published by Mateusz Ratman

High school student from Warsaw, Poland. JHU Class of 2026.

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