Black Hole Scattering and Partition Functions

Abstract

When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by "renormalizing" the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev formula, fixes the reference free energy to be that on a Rindler space, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static BTZ, Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.

Published version. Typos corrected

References in corpus (2)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

Cited by in corpus (10)

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• Is the Euclidean path integral always equal to the thermal partition function?
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• De Sitter entropy: on-shell versus off-shell
• De Sitter Horizon Edge Partition Functions
• Gravitons on Nariai Edges