Late-time tail of a coupled scalar field in the background of a black hole with a global monopole

TL;DR

This paper studies how coupled scalar fields decay over time around a black hole with a global monopole, revealing that coupling affects decay rates at certain times but not at very late times.

Contribution

It provides a detailed spectral decomposition analysis of late-time tails for coupled scalar fields in a black hole with a global monopole, highlighting the impact of coupling on decay rates.

Findings

Massless scalar field decays faster at timelike infinity due to coupling.

Massive scalar field's intermediate late-time decay is accelerated by coupling.

Asymptotic late-time decay rate for massive scalar remains at t^{-5/6}.

Abstract

Using the technique of spectral decomposition, we investigated the late-time tails of massless and massive coupled scalar fields in the background of a black hole with a global monopole. We found that due to existence of the coupling between the scalar and gravitational fields, the massless scalar field decay faster at timelike infinity $i_+$, and so does the massive one in the intermediate late time. But the asymptotically late-time tail for the massive scalar field is not affected and its decay rate still is $t^{-5/6}$.