Stochastic description of near-horizon fluctuations in Rindler-AdS
Abstract
We study quantum spacetime fluctuations near light-sheet horizons associated with a Rindler wedge in anti–de Sitter (AdS) spacetime, in the context of AdS/CFT. In particular, we solve the vacuum Einstein equation near the light-sheet horizon, augmented with the ansatz of a quantum source smeared out in a Planckian width along one of the light-cone directions. Such a source, whose physical interpretation is of gravitational shock waves created by vacuum energy fluctuations, alters the Einstein equation to a stochastic partial differential equation taking the form of a Langevin equation. By integrating fluctuations along the light sheet, we find an accumulated effect in the round-trip time of a photon to traverse the horizon of the Rindler wedge that depends on both the d-dimensional Newton constant G^(d)_N and the AdS curvature L, in agreement with previous literature utilizing different methods.
Copyright and License
Published by the American Physical Society under the terms of the 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.
Acknowledgement
We thank Tom Banks, Temple He, Cynthia Keeler, Vincent Lee, Allic Sivaramakrishnan, and Erik Verlinde for discussion on these directions. We are supported by the Heising-Simons Foundation "Observational Signatures of Quantum Gravity" collaboration Grant No. 2021-2817. The work of K. Z. is also supported by a Simons Investigator grant and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.
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Additional details
- ISSN
- 2470-0029
- Heising-Simons Foundation
- 2021-2817
- Simons Foundation
- United States Department of Energy
- DE-SC0011632
- Caltech groups
- Walter Burke Institute for Theoretical Physics