Chimps said:
I am not convinced by the mathematics of Hawking radiation. I believe it may be flawed.
i'm also skeptical about Hawking Radiation, but only b/c i admittedly know little about the topic. i mean i think i have a grasp on the basic concepts and generalizations, but i have not specifically studied it. i don't have a problem with the existence of Hawking Radiation, but I'm not quite sold on the idea that it always implies a net loss of mass/energy of a black hole, that is, I'm not sold on the whole idea of BH evaporation.
we know that quantum fluctuations occur in the magnetic field of a BH, and that those minute amounts of energy are used to bring particle-antiparticle pairs into existence for infinitesimal time intervals. now i can understand that, if this occurs very near the BH's event horizon, it is entirely possible that one of the particles plunges through the event horizon never to return, while the other escapes to infinity, giving us the impression that the BH is radiating. i also understand that each particle must carry a fraction of the total energy that went into creating them. and so if the total energy taken from the BH's magnetic field in order to create a particle-antiparticle pair is 10, then the sum of the particles' energies is 10...that is, each particle must carry an energy less than the total energy 10 (i left units out for simplicity's sake). so if a BHs' magnetic field gives up a specific amount of energy in creating a particle-antiparticle pair, and the BH swallows one of the particles before the two can annihilate and return the energy to the vacuum, then the BH will have reacquired some, but not all, of the energy that went into creating the particle-antiparticle pair. hence the result is a net loss of mass/energy for the BH.
the things that make me unsure about the above scenario are the assumptions that have to be made in order for things to work out that way. what if we made some other initial assumptions? for instance, what if BOTH particles are swallowed by the BH before they can annihilate? then wouldn't the BH have reacquired ALL of the energy that its magnetic field gave up to create the pair in the first place? it would seem to me that this result has no net gain or loss of mass/energy for the BH, and therefore no evaporation (BH radiation) in this case. also, what about the instance in which the particle-antiparticle pair is produced far enough from the event horizon that neither particle falls in? in this case, it would seem to me that the BH loses the entire amount of energy it put into making the pair in the first place, and is evaporating (radiating) at an increased rate.
considering the above scenarios (and not knowing if all of them are even possible in reality), it would seem to me that in order for a BH to truly evaporate over time, the instances in which both particles of the particle-antiparticle pairs escape the BH would have to occur at approx. the same rate at which the instances in which both particles of the particle-antiparticle pairs fall into the BH occur, thus canceling each other's net effects of mass/energy gain and loss. this leaves only one other type of instance - the one in which one particle of the particle-antiparticle pair falls into the BH, and the other escapes, which yields a net loss of BH mass/energy each time it occurs, and hence results in a BH that truly evaporates over time.
perhaps I'm over-analyzing things - as i said somewhere above, i don't even know if its possible for both particles of an particle-antiparticle pair to fall into a BH,
or for both of them to escape it altogether for that matter. again, those were assumptions i made for a theoretical/mental exercise. if the scenarios i suggested are realistically impossible, then the only scenario left is the one in which one particle fall into the BH, and one escapes it, again yielding a net mass/energy loss for the BH. but i would need someone knowledgeable to show me that the alternative instances which i suggested either do not exist in reality, or do exist, but cancel each other's effects in order to convince me that Hawking Radiation in fact results in the evaporation of a BH over time...