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

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.

References in corpus (8)

• The linear stability of the Schwarzschild solution to gravitational perturbations
• The global non-linear stability of the Kerr-de Sitter family of black holes
• On quasinormal modes of asymptotically anti-de Sitter black holes
• Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces
• Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes
• Linear Stability of the Non-Extreme Kerr Black Hole
• New Dynamics in the Anti-De Sitter Universe AdS^5
• Scattering theory for the Dirac equation on the Schwarzschild-Anti-de Sitter spacetime

Cited by in corpus (2)

• The Stable Trapping Phenomenon for Black Strings and Black Rings and its Obstructions on the Decay of Linear Waves
• Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-Anti-de Sitter spacetime