Negative mode of Schwarzschild black hole from the thermodynamic instability

TL;DR

This paper constructs explicit off-shell negative modes for Schwarzschild black holes, linking thermodynamic instability, such as negative heat capacity, to quantum gravitational off-shell tachyonic modes.

Contribution

It provides the first explicit construction of off-shell negative modes for Schwarzschild black holes inspired by their thermodynamic instability.

Findings

Negative heat capacity correlates with off-shell negative modes.

Constructed modes satisfy boundary conditions like regularity and normalizability.

Supports the connection between thermodynamic and quantum gravitational instabilities.

Abstract

The thermodynamic instability, for example the negative heat capacity, of a black hole implies the existence of off-shell negative mode(s) (tachyonic mode(s)) around the black hole geometry in the Euclidean path integral formalism of quantum gravity. We explicitly construct an off-shell negative mode inspired from the negative heat capacity in the case of Schwarzschild black hole with/without a cosmological constant. We carefully check the boundary conditions, i.e. the regularity at the horizon, the traceless condition, and the normalizability.