Thermal one point functions, large $d$ and interior geometry of black holes

Abstract

We study thermal one point functions of massive scalars in $Ad{S}_{d+1}$ black holes. These are induced by coupling the scalar to either the Weyl tensor squared or the Gauss-Bonnet term. Grinberg and Maldacena argued that the one point functions sourced by the Weyl tensor exponentiate in the limit of large scalar masses and they contain information of the black hole geometry behind the horizon. We observe that the one point functions behave identically in this limit for either of the couplings mentioned earlier. We show that in an appropriate large $d$ limit, the one point function for the charged black hole in $Ad{S}_{d+1}$ can be obtained exactly. These black holes in general contain an inner horizon. We show that the one point function exponentiates and contains the information of both the proper time between the outer horizon to the inner horizon as well as the proper length from the inner horizon to the singularity. We also show that Gauss-Bonnet coupling induced one point functions in $Ad{S}_{d+1}$ black holes with hyperbolic horizons behave as anticipated by Grinberg-Maldacena. Finally, we study the one point functions in the background of rotating BTZ black holes induced by the cubic coupling of scalars.

40 pages, 4 figures, 1 table, reference added, typos corrected

References in corpus (7)

• Towards a derivation of holographic entanglement entropy
• Proper time to the black hole singularity from thermal one-point functions
• Correlation functions in finite temperature CFT and black hole singularities
• Exact thermal correlators of holographic $CFT$s
• Holographic Observables at Large $d$
• Holographic correlation functions at finite density and/or finite temperature
• The Special Role of Toroidal Black Holes in Holography

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• Interior structure of the holographic s + p superconductor and chaotic-stable transition near the black hole singularity
• Finite Temperature at Finite Places
• Proper time to singularity and thermal correlators
• A holographic realization of correlation and mutual information