Temperature Fluctuations and quantum corrections near Black Hole Horizon

TL;DR

This paper explores how temperature fluctuations near a Schwarzschild black hole horizon relate to supertranslations, revealing polynomial corrections to the Euclidean action and a microscopic interpretation via near-horizon symmetries.

Contribution

It establishes a connection between horizon temperature fluctuations and supertranslations, providing a new polynomial functional framework and a microscopic state counting approach.

Findings

Temperature fluctuations are linked to near-horizon supertranslations.

Corrections to Euclidean action are expressed as polynomial functionals of supertranslations.

A near-horizon partition function sums over supertranslations, offering a dual perspective.

Abstract

Spatially varying near-horizon fluctuations of temperature of a Schwarzschild Black Hole is considered within the Euclidean Gravity approach. We present evidence that suggests that such fluctuations in temperature are closely related with the near-horizon supertranslations of a Black Hole. This allows one to express the temperature-dependent corrections to the near-horizon part of the Euclidean gravity action or Free energy in terms of polynomial functionals of a near-horizon supertranslation for all orders. The leading order term turns out to be proportional to the near-horizon supertranslation charge. We also show that this same term results from a microscopic state counting of the near-horizon field with the constraint of near-horizon supertranslation symmetry imposed. The constructed near-horizon partition function provides a physically appealing intuitive description of the low-energy part of horizon physics as a sum over all possible near-horizon supertranslations. This suggests a dual description of near-horizon physics in terms of alternate variables. The implications of these results are briefly discussed.