Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime

TL;DR

This paper constructs precise quasimodes for the Dirac operator in Schwarzschild-Anti-de Sitter spacetime and establishes a logarithmic lower bound on local energy decay, highlighting slow decay behavior.

Contribution

It introduces a method to build exponentially accurate quasimodes for the Dirac operator and derives a new lower bound on energy decay rates in this spacetime.

Findings

Existence of exponentially accurate quasimodes for the Dirac operator.

Logarithmic lower bound for local energy decay in Schwarzschild-Anti-de Sitter spacetime.

Application of Agmon estimates to this setting.

Abstract

We prove the existence of exponentially accurate quasimodes using the square of the Dirac operator on the Schwarzschild-Anti-de Sitter spacetime and the Agmon estimates. We then deduce a logarithmic lower bound for the local energy decay of the Dirac propagator.