Path Integral Over Black Hole Fluctuations

TL;DR

This paper derives a Schrödinger equation for black hole horizon fluctuations by exactly evaluating a functional integral over certain metrics, revealing the existence of blurred horizons and a thermal atmosphere consistent with black hole radiation.

Contribution

It provides a novel exact functional integral approach to quantum fluctuations of black hole horizons, leading to a Schrödinger equation and insights into horizon blurring and thermal atmosphere.

Findings

Establishes probability-preserving current for horizon fluctuations

Demonstrates existence of blurred horizons and thermal atmosphere

Links thermal atmosphere to black hole radiation

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.