Remarks on the thermofield double state in 4D black hole background

Abstract

Recently it was shown that there is an anomalous singularity of propagators in spacetimes with horizons for thermal states with non--canonical temperatures. In this paper we extend these observations to the situation when the background geometry is given by the four--dimensional Schwarzschild and Reissner-Nordström black holes. Namely, we demonstrate that the two-point function in the free scalar field theory acquires anomalous singularity when the two points are located on the horizon. This singularity is anomalous in the sense that the coefficient before the divergent term in the two-point function differs from the canonical one and depends explicitly on the temperature of the state. As it was previously shown, it leads to the explosive behavior of the regularised stress-energy tensor on the horizon when the temperature of the state does not coincide with the canonical temperature of the horizon.

arXiv comment12 pages, 2 figures; V2: email address added, figures resolution fixed; V3: the title has been changed to match the PRD version, typos corrected and clarifications added

References in corpus (13)

• Quasinormal modes of black holes and black branes
• Structure of the black hole's Cauchy horizon singularity
• Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects
• Hawking radiation and secularly growing loop corrections
• Semiclassical effects in black hole interiors
• Two-point function of a quantum scalar field in the interior region of a Reissner-Nordstrom black hole
• Quantum effects near the Cauchy horizon of a Reissner-Nordstrom black hole
• The late-time singularity inside non-spherical black holes
• Propagators and Gaussian effective actions in various patches of de Sitter space
• Heating up an environment around black holes and inside de Sitter space
• Quantum fields in the static de Sitter universe
• Black hole quasinormal modes in the era of LIGO
• A way to distinguish very compact stellar objects from black holes

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• Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime
• Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation
• Is the Euclidean path integral always equal to the thermal partition function?
• De Sitter entropy: on-shell versus off-shell
• Quantization of electromagnetic field in the Schwarzschild spacetime
• Nontrivial self-consistent backreaction of quantum fields in 2D dilaton gravity