Abstract
We show that there is a remarkable phase in quantum gravity where gravitational scattering amplitudes mediated by virtual gravitons can be calculated explicitly in effective field theory, when the impact parameter b satisfies LPl≪b≲RS, with RS being the Schwarzschild radius. This phase captures collisions with energies satisfying s≫γMPl (with γ∼MPl/MBH) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analog where collisions are trans-Planckian. Hawking's geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in 2→2 scattering near the horizon, and explicitly calculate the S-matrix nonperturbatively in MPl/MBH. This involves a resummation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase upon this resummation and is agnostic of Planckian physics and any specific ultraviolet completion. In contrast to the flat-space eikonal limit, the black hole eikonal phase captures collisions of extremely low energy near the horizon.
Original language | English |
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Article number | 026007 |
Journal | Physical Review D |
Volume | 109 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jan 2024 |
Bibliographical note
Publisher Copyright:© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.