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Quantum gravity on the black hole horizon
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abstract
We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in $\hbar$ and $\gamma \sim M_{Pl}/M_{BH}$. These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, $s \gg \gamma^2 M^2_{Pl}$, for semi-classical black holes. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same.
Forward citations
Cited by 2 Pith papers
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Perturbations of Plane Waves and Quadratic Quasinormal Modes on the Lightring
Second-order gravitational perturbations on plane waves are solved with a GHP master equation and tensor harmonics, yielding quadratic quasinormal mode ratios and selection rules.
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Quantum uncertainty in the area of a black hole
The variance of the Schwarzschild horizon area in linearized quantum gravity is computed to be ~ r_H^2 l_P^2, giving a standard deviation ∆A ~ r_H l_P.
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