From bricks to quasinormal modes: A new perspective on black hole entropy

TL;DR

This paper proposes a novel approach to black hole entropy calculation by modeling the horizon as a quantum ergosphere with quasinormal modes, providing a natural regularization mechanism that aligns with the Bekenstein-Hawking result.

Contribution

It introduces a new perspective by linking quasinormal modes to the quantum ergosphere, offering a natural way to regularize entropy calculations without arbitrary cut-offs.

Findings

The quantum ergosphere width sets the entropy cut-off.

Black hole entropy is dual: from quantum field and horizon degrees.

The approach aligns with Bekenstein-Hawking entropy.

Abstract

Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein-Hawking result the short distance cut-off needs to be fixed by hand. In this note we give an argument for obtaining this cut-off in a natural fashion. We do this by modelling the black hole by its set of quasinormal modes. The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.