Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes

TL;DR

This paper investigates scalar tunneling in higher-dimensional black holes, demonstrating the entropy-area relation and exploring thermodynamic properties as the number of dimensions approaches infinity.

Contribution

It provides a unified analysis of tunneling, backreaction, and entropy relations across all spacetime dimensions, including the infinite-dimensional limit.

Findings

Corrections due to backreaction and inverse dimensional expansion are naturally linked.

A simple proof of the entropy-area relation valid in all dimensions is presented.

Thermodynamic quantities relate to the membrane thickness in the infinite-dimensional limit.

Abstract

We study the tunneling of massless scalars across black hole horizons in any number of spacetime dimensions greater than three. Our analysis finds that corrections due to backreaction and the inverse dimensional expansion are naturally concomitant, and furnishes a simple proof of the classic relation between entropy and area in all spacetime dimensions, finite or infinite. We conclude with a discussion of the limit in which the the number of spacetime dimensions is taken to infinity, where we find that thermodynamic quantities are related to the "thickness" of the membrane on which all the curvature is localized.