In all my years of reading and thinking about black holes, one question I've got about HR his how it would actually end up causing the decay of a black hole. From what I understand, HR is the spontaneous creation of matter and anti-matter in space that would normally annihilate itself (allowed by QM theory)--the key difference is that this event can happen at the edge of the event horizon. With some positive probability, the anti-matter will be created within the event horizon radius, but the matter will re
by Anonymous Coward writes:
on Friday October 24, 2014 @10:04AM (#48220377)
There is a generalized conservation of stress-energy-momentum in General Relativity ( you can get a glimpse of it here http://www.preposterousunivers... [preposterousuniverse.com] ).
Essentially, the gravitational field around the black hole is constantly swapping energy with the matter fields around the black hole. We do not know what's happening *in* the black hole, at least not at the very centre, but we are pretty confident about what happens at and outside the horizon. (The AMPS firewalls debate offers up the possibility that semiclassical gravity -- which is what we think happens outside the horizon -- is wrong in some limit. However, it's held up very well under observational tests to date.) However knowing exactly what's on and inside the horizon is not necessary to understand the stress-energy-momentum conservation, because we can see it with other observations at many scales (binary stars, galactic clusters, the metric expansion of space).
Energy donated from the gravitational field of the black hole creates a pair of matter particles. If both are drawn into the black hole, the energy is donated back.
It is exactly equivalent in reverse: high energy in the matter field (from, say, collisions with infalling matter, inverse compton scattering, and so forth) can produce a pair. If both are drawn into the black hole, that energy is donated to the gravitational field.
However, if only one half of the pair stays local and the other escapes to infinity, the local gravitiational field is diminished, whether it's the gravity from inside the event horizon, or very near but outside the horizon.
Likewise, both halves could escape to infinity, again reducing the local gravitational field.
We have good reason to believe that any horizon produces a thermal bath of particles -- Fulling–Davies–Unruh radiation. So right on the horizon there are lots of particles bubbling into existence *because* of the horizon itself. And some amount of that will escape to infinity, reducing the local mass-energy, and thus shrinking the black hole. A retreating horizon produces a greater flux of Unruh radiation, so a shrinking black hole in effect heats up *at the horizon*, which shrinks it further, until it evaporates. Hawking elucidated this process.
For an isolated black hole in various theoretical vacuums, the spectrum of the Hawking radiation is the same as blackbody radiation at a temperature that is entirely determined by the mass-energy of the black hole (or equivalently by the surface area of the horizon).
Stellar black holes and supermassive black holes are unlikely to be isolated, which means that radiation will interact with other matter in the accretion disk and nearby. Indeed, other radiation will be produced within the accretion disk itself, producing e.g. gamma or X rays and particle radiation that are possibly detectable by observatories in our solar system (depends on what gas and dust is between the source and us). When we see such radiation, it's because mass-energy was removed from the black hole system, which shrinks the system. Some *small* amount of that energy will have its origin in the black hole's gravity itself via the stress-energy-momentum conservation law.
How Would Hawking Radiation Dissolve a Black Hole? (Score:3)
In all my years of reading and thinking about black holes, one question I've got about HR his how it would actually end up causing the decay of a black hole. From what I understand, HR is the spontaneous creation of matter and anti-matter in space that would normally annihilate itself (allowed by QM theory)--the key difference is that this event can happen at the edge of the event horizon. With some positive probability, the anti-matter will be created within the event horizon radius, but the matter will re
Re:How Would Hawking Radiation Dissolve a Black Ho (Score:0)
There is a generalized conservation of stress-energy-momentum in General Relativity ( you can get a glimpse of it here http://www.preposterousunivers... [preposterousuniverse.com] ).
Essentially, the gravitational field around the black hole is constantly swapping energy with the matter fields around the black hole. We do not know what's happening *in* the black hole, at least not at the very centre, but we are pretty confident about what happens at and outside the horizon. (The AMPS firewalls debate offers up the possibility that semiclassical gravity -- which is what we think happens outside the horizon -- is wrong in some limit. However, it's held up very well under observational tests to date.) However knowing exactly what's on and inside the horizon is not necessary to understand the stress-energy-momentum conservation, because we can see it with other observations at many scales (binary stars, galactic clusters, the metric expansion of space).
Energy donated from the gravitational field of the black hole creates a pair of matter particles. If both are drawn into the black hole, the energy is donated back.
It is exactly equivalent in reverse: high energy in the matter field (from, say, collisions with infalling matter, inverse compton scattering, and so forth) can produce a pair. If both are drawn into the black hole, that energy is donated to the gravitational field.
However, if only one half of the pair stays local and the other escapes to infinity, the local gravitiational field is diminished, whether it's the gravity from inside the event horizon, or very near but outside the horizon.
Likewise, both halves could escape to infinity, again reducing the local gravitational field.
We have good reason to believe that any horizon produces a thermal bath of particles -- Fulling–Davies–Unruh radiation. So right on the horizon there are lots of particles bubbling into existence *because* of the horizon itself. And some amount of that will escape to infinity, reducing the local mass-energy, and thus shrinking the black hole. A retreating horizon produces a greater flux of Unruh radiation, so a shrinking black hole in effect heats up *at the horizon*, which shrinks it further, until it evaporates. Hawking elucidated this process.
For an isolated black hole in various theoretical vacuums, the spectrum of the Hawking radiation is the same as blackbody radiation at a temperature that is entirely determined by the mass-energy of the black hole (or equivalently by the surface area of the horizon).
Stellar black holes and supermassive black holes are unlikely to be isolated, which means that radiation will interact with other matter in the accretion disk and nearby. Indeed, other radiation will be produced within the accretion disk itself, producing e.g. gamma or X rays and particle radiation that are possibly detectable by observatories in our solar system (depends on what gas and dust is between the source and us). When we see such radiation, it's because mass-energy was removed from the black hole system, which shrinks the system. Some *small* amount of that energy will have its origin in the black hole's gravity itself via the stress-energy-momentum conservation law.