How Does Hawking Radiation Affect Black Hole Energy Loss?

[jezz78]

Hello, I am a newbie to these forums, so please be patient with me! OK, my first (but not only) problem is getting to understand Black Hole physics... I understand they (BHs) arise as solutions to the EFE's, and there are currently many efforts to tie in Quantum Theory in a consistent way which should be able to clarify our current models somewhat. Hawkings' proposed radiation due to the uncertainty principle is fascinating, my questions for today :- BHs always lose energy due to Hawking radiation which should be detected as +ve energy mode photons emitted away from the event horizon. Now, would this energy be seen as a continuous stream of energy (ie. consistent radiation around the whole sphere of the BH) or would it be "patchy" or variating (due to the uncertainty principle fluctuations and the gravitation field strength) causing areas of high / low energy loss? Also, is it possible that due to the uncertainty principle the BH could spontaneously shed a sudden very high amount of energy, which might be seen as a burst of radiation (and presumably a corresponding decrease in the BH's mass)? Basically my understanding of the undertainty principle is that it gives an upper-bound on certainty, but could this prevent a BH from shedding most or even all of it's mass in a single burst of Hawking Radiation, given the right conditions? I know micro-BHs will (in theory) evaporate very very quickly, could massive or supermassive BHs be able to evaporate in similar time scales or is this prohibited by the HR mechanism/ uncertainty bounds? Many thanks, apologies if I have been vague, if you wish I will ask my questions with equations rather than words.

 

[Chronos]

Hawking radiation is extraordinarily difficult to detect under normal circumstances. It is overwhelmed by other sources, like the CMB - which is many times more intense. Only a tiny black hole would emit enough to be detectable, and we are by no means sure tiny holes even exist. We have not yet detected Hawking radiation, although some interesting experiments are in the works.

 

[jezz78]

Chronos - your answer is platonic insofar as you only talk about BH radiation in the context of actually detecting it. My question was aimed more towards the proposed mathematics of the radiation itself, I presume there are complete models of the expected radiation pattern (composed of x-rays) and basically I'm concerned with the possibility that the uncertainty principle might allow variations in the rate of radiation, meaning that there could be BHs giving off occasional pulses of high energy radiation (although I accept that this would be unlikely wrt a stable radiation rate model). Also, what would be the geometric properties of the space-time immediately in the vicinity of the event horizon, given that the uncertainty principle shows a "space-time foam" composition, would this "foam" effect also apply to the geometry of the event-horizon itself, ie. would the event-horizon be changing/fluctuating in shape at it's boundary due to the U-Princ? thanks.

 

[twofish-quant]

I'm concerned with the possibility that the uncertainty principle might allow variations in the rate of radiation, meaning that there could be BHs giving off occasional pulses of high energy radiation (although I accept that this would be unlikely wrt a stable radiation rate model).

It couldn't. Something about black holes is that no information can leave the black hole. Therefore there is nothing that the black hole can do that would cause a burst of radiation. You can do statistics to figure out the variation of the radiation that is being produced and there isn't anything other than quantum randomness.

Also, what would be the geometric properties of the space-time immediately in the vicinity of the event horizon, given that the uncertainty principle shows a "space-time foam" composition, would this "foam" effect also apply to the geometry of the event-horizon itself, ie. would the event-horizon be changing/fluctuating in shape at it's boundary due to the U-Princ? thanks.

No. Weird things happen near the singularity, but nothing unusual happens near the event horizon.

 

[jezz78]

OK I think I'm beginning to get the picture with BHs - thanks for the help, the No-Hair theorem is quite tidy and pretty much covers what we have discussed. Thanks for helping clarify my problems with "unpredictability" and Black Holes - black holes are quite stable systems near their event horizons (ie. what we see is what we get) I can accept that the Hawking Radiation would be very hard to detect, and that any UP effects wouldn't significantly amount anything more than a very small amount of quantum randomness (Vacuum field energy) - the event horizon's gravitation would be homogeneous and one black hole with certain properties will be pretty much identical in behaviour as any other with the same properties. Does this mean that BHs could be used as "cepheid variables", in other words could these "invariant" properties of BHs be so special as to allow them to be used as a gague to infer the behaviour of physical phenomena elsewhere in the universe? (for instance high energy gravitation?) I suspect BHs have a lot to offer us in confirming physical models and field theories. Many Thanks.