Scalar Wave Falloff in Asymptotically Anti-de Sitter Backgrounds

TL;DR

This paper investigates how conformally invariant scalar waves decay in asymptotically anti-de Sitter black hole spacetimes, revealing different decay patterns in 2+1 and 3+1 dimensions with implications for mass inflation.

Contribution

It provides analytical and numerical analysis of scalar wave decay in asymptotically AdS black holes, highlighting dimension-dependent falloff behaviors.

Findings

Exponential decay in (2+1)-dimensional black hole background.

Non-exponential, non-inverse power decay in (3+1)-dimensional Schwarzschild-AdS.

Weakly exponential falloff of the maximal peak in 3+1 dimensions.

Abstract

Conformally invariant scalar waves in black hole spacetimes which are asymptotically anti-de Sitter are investigated. We consider both the $(2+1)$-dimensional black hole and $(3+1)$-dimensional Schwarzschild-anti-de Sitter spacetime as backgrounds. Analytical and numerical methods show that the waves decay exponentially in the $(2+1)$ dimensional black hole background. However the falloff pattern of the conformal scalar waves in the Schwarzschild-anti-de Sitter background is generally neither exponential nor an inverse power rate, although the approximate falloff of the maximal peak is weakly exponential. We discuss the implications of these results for mass inflation.