Is it possible to have a stable black hole that does not evaporate?

Question

Black holes would presumably evaporate in the long future via Hawking radiation.

However is this inevitable? Or are there any mechanisms that would compensate the lost mass due to Hawking radiation avoiding the evaporation of certain black holes?

It was recently observed that apparenlty black holes increase their mass as the universe expands (https://newatlas.com/physics/dark-energy-black-holes-accelerate-expansion-universe/ ; https://www.space.com/black-holes-expanding-with-universe). However, these results are still preliminary. So I was looking for something more grounded.

Perhaps if a black hole had a long standing and stable accretion disk with a low infall rate all the mass lost could be compensated by the disk radiation and matter falling towards the black hole (assuming that the universe had no CMB radiation that would also infall to the black hole, altering this equilibrium)?

Answer 1

It's probably inevitable. However, it's not really possible to make any completely definitive statements about Hawking radiation because it's a quantum process involving general relativity, and we don't yet have a consistent theory of quantum gravity. But let's assume that Hawking's derivation is basically correct...

The Hawking radiation temperature of a black hole is inversely proportional to its mass. Even stellar mass BHs are very cold, so they radiate very slowly, and the supermassive BHs at the hearts of most galaxies are even colder.

According to Viktor Toth's Hawking radiation calculator, a 5 solar mass BH, which has a Schwarzschild radius of ~14.770 km, has a Hawking temperature of 1.23374e-8 K and an expected lifetime of 1.44968e69 years.

However, the cosmic microwave background (CMB) radiation is currently 2.73 K, which is over 200 million times hotter than the 5 solar mass BH. So in the present era, black holes are absorbing more energy than they radiate. The CMB cools as the universe expands, but it will take around 1e29 years before the CMB is cooler than even the smallest BHs that can be formed via core-collapse supernovae. And of course those BHs will continue to grow and get colder in the intervening years.

It's currently around 13.7 billion years since the Big Bang, but that's less than an eyeblink compared to 1e29 years. And that's less than an eyeblink compared to 1.4e69 years. So even though black holes won't start losing mass until the universe is more than a billion billion times its current age, the evaporation time is so long that that delay is effectively negligible. ;)

By the time the BH evaporation era begins there won't be much else left in the universe, except maybe a few neutron stars and black dwarfs that haven't yet fallen into a black hole. There definitely won't be any remaining accretion disks. There may still be some stray matter floating around, but if so, it will be extremely diffuse.

Wikipedia has an interesting timeline of the far future, but it includes some speculative things, like proton decay, and it's not completely self-consistent.

Answer 2

Extremal black holes have a Hawking temperature of zero and an infinite lifetime in theory.

The lifetime of large black holes is long enough that it's plausible that the universe will end in another way before they evaporate completely.

I think those are the only two options.

Perhaps if a black hole had a long standing and stable accretion disk with a low infall rate all the mass lost could be compensated by the disk radiation and matter falling towards the black hole

If you have an external source of matter to stave off the evaporation, you are better off tossing it in as soon as possible since it will reduce the evaporation rate.

If you're imagining a closed system where the radiation is captured and falls back in, that won't work because of the second law of thermodynamics. In the long term everything near the hole will end up at a uniform temperature and radiating outward at that temperature, and it will be the Hawking temperature.

It was recently observed that apparently black holes increase their mass as the universe expands

That's very unlikely to be true. I wrote this answer and this answer and this answer about it.

Answer 3

This is not realizable (easily) I think in our Univese:

If you have a (either a sufficiently large) blackhole on a (or a sufficiently small) compact manifold for your universe, then the hawking radiation it emits should in some critical time $T$ be expected to collide again and be re-absorbed by the blackhole. As long as the rate of re-absorption is greater than or equal to the rate of evaporation this would be an eternally stable blackhole.

If I had a better command on the mathematics of GR I would've liked to describe this. I don't think you even need to know any QFT just, you can assume the blackhole emits photons according to the blackbody spectrum uniformly for all directions on its surface, so this becomes a pure Geometry + probability type of problem.

Answer 4

According to current theories, all black holes must evaporate over time, as the laws of physics as we currently know them really won't let anything last truly forever. That said, it is possible to have black holes that evaporate so slowly that on human timescales, it appears they don't evaporate at all.