Abstract
We study holographic renormalization group (RG) flows perturbed by a shock wave in dimensions d ≥ 2. The flows are obtained by deforming a holographic conformal field theory with a relevant operator, altering the interior geometry from AdS-Schwarzschild to a more general Kasner universe near the spacelike singularity. We introduce null matter in the form of a shock wave into this geometry and scrutinize its impact on the near-horizon and interior dynamics of the black hole. Using out-of-time-order correlators, we find that the scrambling time increases as we increase the strength of the deformation, whereas the butterfly velocity displays a non-monotonic behavior. We examine other observables that are more sensitive to the black hole interior, such as the thermal a-function and the entanglement velocity. Notably, the a-function experiences a discontinuous jump across the shock wave, signaling an instantaneous loss of degrees of freedom due to the infalling matter. This jump is interpreted as a ‘cosmological time skip’ which arises from an infinitely boosted length contraction. The entanglement velocity exhibits similar dependence to the butterfly velocity as we vary the strength of the deformation. Lastly, we extend our analyses to a model where the interior geometry undergoes an infinite sequence of bouncing Kasner epochs.
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Acknowledgments
We would like to thank José Barbón, César Gómez and Karl Landsteiner for interesting discussions and comments on the manuscript. The work of EC is supported by the National Science Foundation under grant number PHY-2112725. AKP and JFP are supported by the ‘Atracción de Talento’ program (Comunidad de Madrid) grant 2020-T1/TIC-20495, by the Spanish Research Agency via grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/501100011033, and by ERDF A way of making Europe. EC thanks the Instituto de Física Teórica UAM/CSIC, Madrid, for hospitality during the initial stages of this work.
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Cáceres, E., Patra, A.K. & Pedraza, J.F. Shock waves, black hole interiors and holographic RG flows. J. High Energ. Phys. 2024, 52 (2024). https://doi.org/10.1007/JHEP07(2024)052
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DOI: https://doi.org/10.1007/JHEP07(2024)052