# How Do Black Holes Evaporate?

## Quantum Time

In the mid-1970s, Stephen Hawking was able to show that black holes are not just drawing in material and giving nothing back. When one looks at Minkowski space (flat), the picture was traditional: eat, eat, eat and give nothing back. But Hawking looked at black holes in Schwarzschild space (curved) and found otherwise. Turns out, black holes emit something called Hawking radiation (HR) which result from the curved space generating blackbody radiation via the vacuum energy around a black hole, creating a set of virtual particles, with one of the pair falling into the singularity while the other escapes away. Because of this quantum mechanics principle and the conservation of energy, the black hole must lose mass in this process because energy escaped in the form of a virtual particle, and mass is energy (roughly). Opposite pairs of virtual particles that escape the black hole combine to form real photons, with the energy needed for it being supplied by the pair inside the black hole. Thus, as time progresses black holes will shrink and shrink until they disappear! (Baez, Siegel 05 Dec.)

But how can we witness this to confirm our theory? Well, the smaller the black hole the more rapidly it is shrinking, so we want to find one of low mass. Based on the known age of the Universe in 1980 (10-20 billion years), the black hole would need to be smaller than 10^{15} grams otherwise it would be too big to have evaporated. With that kind of mass, we are looking at a black hole with an event horizon of about…10^{-31 }meters. So, the chance of spotting one isn’t very good (Shipman 117-9).

Well, maybe we can spot some other sign of evaporating black holes. And the answer is yes. Around many black holes is an accretion disc of matter falling in, and as the HR emanates outward the black hole shrinks and causes the radius of the event horizon to decrease. With conservation of angular momentum at play, the material spins faster, colliding and producing gamma rays of a frequency and intensity so high modern tech cannot see…yet (Shipman 120).

## Longevity

And the lifespan of an evaporating black hole? A complicated question, relating to the speed that material falls in and the size of a black hole at any given point. The material falling in is what supplies the energy for Hawking radiation to occur in the first place and so the more it falls in the faster the evaporation occurs. Yes, the radiation does occur at a minimal level just by having the black hole move, but it would take 10^{71} years for a solar mass black hole to disappear. Material falling in does cause the mass to grow but eventually the black hole clears its area of space and then evaporation wins out (Siegel 05 Dec.).

But a very subtle but major issue arises when we talk about a lifespan of black holes. What happens to everything the black hole accumulated? Information cannot be lost, according to quantum physics, so what actually happens? To fully understand that, scientists need quantum gravity to deal with both relativity and quantum mechanics, but scientists at the University of Ottawa and MSU have run a simulation to try and parse something together. Chris Adami and Kamil Bradler set up a simulation that looked at the latter stages of a black holes life, and it showed that the information contained in the black hole was slowly released as the black hole evaporated via Hawking radiation. Their model correlated well with the anticipated Page curves which predict how information enters and leaves a system, so that give the model some credence (Ward).

And the very end of a black holes life would be spectacular. After evaporating for countless years, the last second arrives. Evaporation has taken all but 228 metric tons of the black hole, whose event horizon is now 3.4*10^{-22} meters in size. This is roughly 2.05*10^{22} Joules of energy here, and the final second sees that evaporated into space as the singularity is removed and space-time at that location is restored. Lots of light will befall the region and then…nothingness. Such is the ironic end to an evaporating black hole: no one ever knows it was there (Siegel).

## Works Cited

Baez, John. “Hawking Radiation.” *Math.ucr.edu*. 1994. Web. 04 Oct. 2017.

Shipman, Harry L. Black Holes, Quasars, and the Universe. Boston: Houghton Mifflin, 1980. Print. 117-120.

Siegel, Ethan. “Ask Ethan: How Do Black Holes Really Evaporate?” *Forbes.com*. 05 Dec. 2015. Web. 03 Oct. 2017.

---. “Ask Ethan: What Happens When a Black Hole’s Singularity Evaporates?” *Forbes.com*. 20 May 2017. Web. 05 Oct. 2017.

Ward, Kim. “Solving the Mystery of Evaporating Black Holes.” *Msutoday.msu.edu*. Michigan State University, 09 March 2016. Web. 05 Oct. 2017.

**© 2018 Leonard Kelley**

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