Negative modes of Schwarzschild black hole in Einstein-Gauss-Bonnet Theory

TL;DR

This paper investigates the negative modes of Schwarzschild black holes in five-dimensional Einstein-Gauss-Bonnet gravity, revealing conditions under which negative modes exist and their potential physical implications.

Contribution

It identifies the presence and number of negative modes for Schwarzschild black holes in Einstein-Gauss-Bonnet theory across different parameter regimes, extending previous understanding from Einstein gravity.

Findings

A unique negative mode for black holes with negative heat capacity.

Additional negative modes exist for small black holes with positive heat capacity.

No negative modes are found in regions where the heat capacity is positive.

Abstract

We study non conformal negative modes of Schwarzschild black holes in the five dimensional Einstein-Gauss-Bonnet gravity theory with a zero or negative cosmological constant, in the context of the semiclassical quantum gravity formulated by the path integral. We find an unique negative mode when the black hole has a negative heat capacity which is the same in Einstein theory. On the other hand, we still find negative modes inside a parameter region where a small black hole has a positive heat capacity. The number is one/two for the case of zero/negative cosmological constant respectively. In the rest of the parameter region where the heat capacity is positive, we find no negative modes. We discuss the possible physical understanding of having one or two negative modes.