# Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-Anti-de Sitter spacetime

## TL;DR

This paper derives an explicit formula for the resolvent of the massive Dirac operator in Schwarzschild-Anti-de Sitter spacetime and extends it meromorphically across the real axis, providing insights into its spectral properties.

## Contribution

It provides the first explicit formula for the resolvent and its meromorphic extension for the massive Dirac operator in this spacetime setting.

## Key findings

- Explicit resolvent formula derived
- Meromorphic extension achieved across the real axis
- Enhanced understanding of spectral properties of the operator

## Abstract

We study the resolvent of the massive Dirac operator in the Schwarzschild-Anti-de Sitter space-time. After separation of variables, we use standard one dimensional techniques to obtain an explicit formula. We then make use of this formula to extend the resolvent meromorphically accross the real axis.