Radiative falloff in Schwarzschild-de Sitter spacetime

TL;DR

This paper studies the time evolution of scalar fields in Schwarzschild-de Sitter spacetime, revealing different decay behaviors at early, intermediate, and late times, influenced by spacetime structure and coupling constants.

Contribution

It provides a detailed analysis of scalar field decay patterns in Schwarzschild-de Sitter spacetime, highlighting the influence of spacetime regions and the curvature-coupling constant on late-time behavior.

Findings

Early times: pure Schwarzschild behavior with quasi-normal oscillations.

Intermediate times: transition to exponential decay.

Late times: pure de Sitter behavior with decay dependent on xi.

Abstract

We consider the time evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from the black hole has no influence on the evolution. In this early epoch, the field's initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At intermediate times, the power-law behavior gives way to a faster, exponential decay. At late times, the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the field's behavior depends on the value of the curvature-coupling constant xi. If xi is less than a critical value 3/16, the field decays exponentially, with a decay constant that increases with increasing xi. If xi > 3/16, the field oscillates with a frequency that increases with increasing xi; the amplitude of the field still decays exponentially, but the decay constant is independent of xi.