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I have nearly finished reading the book “Black Holes” by Brian Cox and Jeff Forshaw and can highly recommed it. I was very pleased that I now have an understanding of “Penrose Diagrams” and “The Kerr Solution”. However I started to lose the plot around chapters 9 and 10 when Quantum Mechanics started to make an appearance as Hawking radiation was introduced. I have a couple of questions:-
1. How does Hawking radiation appear to the observer falling into a large black hole where tidal forces at the event horizon are tolerable?
Virtual partical pairs are subject to the uncertainty principle whereby (Delta)E x (Detla)t <= h/2 so the (presumably) large energy required to escape the black hole can only be “borrowed” for a very short time so what force succeeds in separating them before re-combination if tidal forces are weak and why don’t we see this process happening in our low tidal gravitational field on Earth? shouldn’t the Earth evaporate?
2. Given that the only (as far as I know) other result obtained by combining quantum fluctuations and General Relativity i.e. calculation of the Cosmological Constant, disagrees with observation by a factor of 10^120 how confident should we be that Hawking radiation exists?
I know (but don’t understand!) that “supersymmetry” would yield a more realistic Cosmological Constant but how would this affect Hawking radiation?
1. One-word answer: temperature. The smaller the gravitational field gradient the less likely a virtual particle pair (not restricted to photons by the way) is to be split into real particles and the lower the energy carried by each. As photons have zero rest mass there is no lower limit to their energy, which corresponds to no lower limit to the temperature of the BH. All sufficiently massive black holes have a very low temperature. A solar mass BH, for example, has a Hawking temperature much much lower than that of the cosmic background and is absorbing those photons, thus slowly gaining more mass from them than it is losing from Hawking radiation. The hypothetical observer would see the CBR as being much much more intense than the Hawking radiation which would be swamped completely by the background.
2. There is no good theory of quantum gravity as yet. The naive calculation is almost certainly wrong. Further, Hawking radiation has yet to be observed because all known black holes are far too massive to emit significant levels of radiation.
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