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Synthetic fuzzballs: a linear ramp from black hole normal modes

Das, S and Krishnan, C and Kumar, AP and Kundu, A (2023) Synthetic fuzzballs: a linear ramp from black hole normal modes. In: Journal of High Energy Physics, 2023 (1).

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Official URL: https://doi.org/10.1007/JHEP01(2023)153


We consider a black hole with a stretched horizon as a toy model for a fuzzball microstate. The stretched horizon provides a cut-off, and therefore one can determine the normal (as opposed to quasi-normal) modes of a probe scalar in this geometry. For the BTZ black hole, we compute these as a function of the level n and the angular quantum number J. Conventional level repulsion is absent in this system, and yet we find that the Spectral Form Factor (SFF) shows clear evidence for a dip-ramp-plateau structure with a linear ramp of slope ~ 1 on a log-log plot, with or without ensemble averaging. We show that this is a robust feature of stretched horizons by repeating our calculations on the Rindler wedge (times a compact space). We also observe that this is not a generic feature of integrable systems, as illustrated by standard examples like integrable billiards and random 2-site coupled SYK model, among others. The origins of the ramp can be traced to the hierarchically weaker dependence of the normal mode spectrum on the quantum numbers of the compact directions, and the resulting quasi-degeneracy. We conclude by noting an analogy between the 4-site coupled SYK model and the quartic coupling responsible for the non-linear instability of capped geometries. Based on this, we speculate that incorporating probe self-interactions will lead to stronger connections to random matrix behavior. © 2023, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH.
Keywords: Black Holes; Black Holes in String Theory; Models of Quantum Gravity; Random Systems
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 16 Feb 2023 05:28
Last Modified: 16 Feb 2023 05:28
URI: https://eprints.iisc.ac.in/id/eprint/80314

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