Path Integral Over Black Hole Fluctuations

Abstract

Evaluating a functional integral exactly over a subset of metrics that represent the quantum fluctuations of the horizon of a black hole, we obtain a Schroedinger equation in null coordinate time for the key component of the metric. The equation yields a current that preserves probability if we use the most natural choice of functional measure. This establishes the existence of blurred horizons and a thermal atmosphere. It has been argued previously that the existence of a thermal atmosphere is a direct concomitant of the thermal radiation of black holes when the temperature of the hole is greater than that of its larger environment, which we take as zero.

5 pages, added a couple of clarifications

References in corpus (2)

• Black hole entropy in Loop Quantum Gravity
• Relationship between Hawking Radiation and Gravitational Anomalies

Cited by in corpus (7)

• Stochastic Gravity: Theory and Applications
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
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• Analytic structure of radiation boundary kernels for blackhole perturbations
• Quantum Black Hole Wave Packet: Average Area Entropy and Temperature Dependent Width
• Quasi-Local Energy of a Charged Rotating Object Described by the Kerr-Newman Metric
• Quantum wormholes at spatial infinity