Counting the negative eigenvalues of the thermalon in three dimensions

TL;DR

This paper studies the thermalon in three dimensions, analyzing its negative eigenvalues to understand membrane nucleation and black hole formation, with a focus on the effects of gravity on its spectral properties.

Contribution

It extends the analysis of the thermalon to three-dimensional spacetime, examining how gravity influences the number of negative eigenvalues in the one-loop structure.

Findings

Coupling to gravity can increase the number of negative eigenvalues.

Analysis avoids issues from propagating gravitational degrees of freedom.

Provides insights into membrane nucleation and black hole formation in 3D.

Abstract

Some years ago it was shown that the cosmological constant may be reduced by thermal production of membranes that, after nucleation, collapse into a black hole. The probability of the process was calculated in the leading semiclassical approximation by studying an associated Euclidean configuration called the thermalon. Here we investigate the thermalon in three spacetime dimensions, describing the nucleation of closed strings that collapse into point particle singularities. In this context we may analyze the one-loop structure without the well known problems brought in by the propagating gravitational degrees of freedom. We found that the coupling to gravity may increase the number of negative eigenvalues of the operator.