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Suppose a particle with mass m falls radially from rest in flat space to the event horizon of a Schwarzschild black hole without losing anything to radiation. How much energy (mass) does it contribute? Obviously it is not infinite, despite the common assertion that it reaches the speed of light. So presumably it either becomes massless or enters at less than c. I'm assuming it actually does pass the horizon, although that can't be verified by direct observation.

It doesn't add anything, simply because there is no information loss. The particles after passing the event horizon will immediately tunnel back into the vacuum.

Quote from: Mr. Scientist on 01/12/2009 22:31:16It doesn't add anything, simply because there is no information loss. The particles after passing the event horizon will immediately tunnel back into the vacuum.That is an unusual view (unless referring to Hawking radiation, but that is not what the question is about) and not one I've come across except, perhaps, as highly speculative ideas regarding a BH being a wormhole to a WH. Have you any reference that supports this hypothesis?The (Schwarzschild) EH of a BH is really only defined from infinity or, at least, a long way off. A mass would only attain a theoretical infinite value if falling from that distance. A mass sufficiently close to what we, at a great distance see as a BH, may not see a BH at all. Local mass can be collected by a BH in order to form it but mass falling from a distance, such that an observer close to the mass could see the BH Event Horizon, would see the mass approach the EH, but Time Dilation and Doppler shift would result in the mass never crossing the EH from the observer's perspective. The nasty infinity is effectively cosmically censored :-)

Re-reading what I said previously, I gave the impression that the mass would not cross the EH, but it will if on a perfect trajectory. It is just that you can't see it cross. The mass (and diameter) of the BH will increase accordingly, and this should include the mass due to object's velocity also. If the mass originates from a position from which you can observe an EH then I can't see why this would not correspond to an infinite mass gain for the BH either, as observed from the starting point. As I said, good question. Perhaps someone else has a view.Mr S, If BH's exist, which is not certain though evidence points that they do, then mass must have got in there and not immediately "tunneled" out by some means. I could not find any paper that describes the phenomena you postulate. If you can point to some reputable journal where this is described I would be most interested.

Well, I'll try again. The fact that we never see anything cross the EH is irrelevant. Use isotropic coordinates and it crosses.I don't care how long it stays.I'm just asking how much mass/energy it adds to the BH. Assuming there are large black holes -- which is reasonably well confirmed by observation -- they must have accreted their mass/energy from stuff crossing the horizon. Their mass/energy is neither zero nor infinity. Therefore a particle crossing the EH must contribute some particular (within Heisenberg limits) energy. Someone must know how to compute it, hopefully someone here. I don't, and sure would like to find out.

itisus, your question is a good one and I don't know the answer. It may well be that nobody does exactly but I expect there are a lot of theories. It is not certain what is meant by mass itself (gravitational or inertial) or how much the mass of a body we observe is actually the energy of the gravitational scalar field. I think the easiest way to think about this is to consider only a two body problem of an object and a non-rotating black hole. An inert observer being permitted..... However this seems in contradiction to the finite potential energy at which the two objects start off.

How much mass would it add... It's not longer part of our universe if that be the case, and black holes are not closed systems internally. Then of course there is the speed at which the particle is moving at, then there is the mass of the black hole in question as well.

Quote from: Mr. Scientist on 04/12/2009 08:22:26How much mass would it add... It's not longer part of our universe if that be the case, and black holes are not closed systems internally. Then of course there is the speed at which the particle is moving at, then there is the mass of the black hole in question as well.What do you mean by "not closed systems internally"?By "not longer part of our universe," I assume you mean it is behind the horizon. But it's mass, rotation, and charge are still available. I hope entropy is not relevant here.

But if you are hanging on the event horizon, not falling, you will say that the stuff that is falling from above has infinite energy.When an object with infinite energy has fallen past you into the black hole, you will say that an infinite increase of black hole's mass occurred when the object with infinite mass plunged there.

Do you guys understand simple stuff?