Telling Tails In The Presence Of A Cosmological Constant

TL;DR

This paper investigates how massless scalar waves decay over time in black hole spacetimes with a positive cosmological constant, revealing exponential decay and unique asymptotic behaviors, with implications for black hole horizon stability.

Contribution

It demonstrates the existence of exponentially decaying tails for scalar waves in Schwarzschild-de Sitter and Reissner-Nordstrom-de Sitter spacetimes and compares analytical and numerical results for the l=0 mode.

Findings

Scalar waves exhibit exponential decay at late times.

The l=0 mode approaches a non-zero value, unlike in flat spacetime.

Numerical and analytical results agree well for the l=0 mode.

Abstract

We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a non-zero cosmological constant. Considering test fields on both Schwarzschild-de Sitter and Reissner-Nordstrom-de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly the l=0 mode asymptotes to a non-zero value, contrasting the asymptotically flat situation. We also compare these results, for l=0, with a numerical integration of the Einstein-Scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black hole-de Sitter spacetimes is discussed.