Abstract
Quantum black holes are difficult to describe. We consider two seemingly divergent approaches, high-energy scattering and the proposal to regard black holes as Bose-Einstein condensates of gravitons, and establish a connection between them. Results from the eikonal approximation of high-energy scattering are reconsidered and processed further by a saddle-point approximation. The dominant contribution to the scattering amplitude comes from a ladder diagram with the exchange of N gravitons, and the number of gravitons follows a Poisson distribution. This approximation supports the picture of a graviton Bose-Einstein condensate with an extent equal to the Schwarzschild radius, which grows with N in a way determined by the saddle point. The approach permits calculations of 1/N corrections from the fluctuations around the saddle points and we comment on these. Scattering methods might be useful probes of quantum black holes, especially when interpreted in terms of condensates.
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Kühnel, F., Sundborg, B. High-energy gravitational scattering and Bose-Einstein condensates of gravitons. J. High Energ. Phys. 2014, 16 (2014). https://doi.org/10.1007/JHEP12(2014)016
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DOI: https://doi.org/10.1007/JHEP12(2014)016