On JT gravity path integrals and the tunneling process

TL;DR

This paper explores the interpretation of JT gravity path integrals involving complex geometries, revealing the necessity to consider moduli space contributions to understand black hole transitions and baby universe emissions.

Contribution

It extends the understanding of JT gravity path integrals to higher genus geometries, emphasizing the role of moduli space in interpreting black hole transitions.

Findings

Path integrals for higher genus geometries require moduli space considerations.

Interpretation as black hole transition amplitudes extends beyond simple geometries.

Moduli space contributions are essential for a complete understanding of these processes.

Abstract

The Jackiw-Teitelboim (JT) gravity path integral of the trumpet can be interpreted as a transition amplitude from an older black hole to a younger one, accompanied by the emission of a baby universe, represented by the geodesic boundary of the trumpet. However, this interpretation becomes less straightforward for geometries with higher genus and multiple geodesic boundaries. In this paper, we examine the path integral for these more complex geometries and find that maintaining this interpretation requires accounting for a portion of the moduli space.