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Gravitational force is mediated by graviton exchange. If I am standing outside a black hole, I can of course feel the attracting force towards the black hole. This should correspond to gravitons mediated between the matter inside the horizon and myself; but then these gravitons should cross the horizon from the inside to the outside.

My question is: how is this paradox precisely solved?

I guess a starting point for an answer is that these gravitons are off-shell, much like in QED where photons exchanged between electrons that feel each other are virtual. But still, this confuses me a bit - is there some references explaining this in detail?

arovai
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  • You can't think of gravitons with Black Holes, because that's naively putting a quantum theory in GR, which we don't know how to resolve yet. – Chris Gerig Jun 25 '13 at 07:13
  • @ChrisGerig: gravitons are appearing already at the semi-classical approximation of gravity, which is meaningful even if it is a non-renormalisable theory (think for example about Fermi theory - you still draw three level graphs and so on, although it is non-renormalisable). Of course in this case we are interested in gravitons seen as perturbation around a non-trivial solution of the equation of motion, but still, semi-classical approximation make sense. – arovai Jun 25 '13 at 07:27
  • Semi-classical gravity breaks down for black holes. – Chris Gerig Jun 25 '13 at 07:34
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    Possible duplicate of How does gravity escape a black hole? – John Rennie Jun 25 '13 at 08:39
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    In some special cases, it is clear that there is no paradox: For a fixed outside observer, there is nothing beyond the horizon, so there is no paradox. For a free falling outside observer, he is a inertial observer, so he does not feel gravitation, so there is no paradox too. – Trimok Jun 25 '13 at 08:48
  • @ChrisGerig: well, semi-classical approximation means that you consider quantum fluctuations at first order around a classical solution of the equations of motions. A particular case of this is when you expand around the vacuum, but you may well expand around other non-trivial solutions. This is done for example in non-abelian euclidean YM theory, where typically you compute progapators and so on in an instanton background. JohnRennie: thanks, I'll have a look. – arovai Jun 25 '13 at 08:49
  • No the point is that the theory isn't valid for large mass. Also this "paradox" has been asked many times on the Internet, you should be checking that out. – Chris Gerig Jun 25 '13 at 09:17

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