Decay of massive scalar field in a Schwarzschild background

TL;DR

This paper analyzes the decay of massive scalar fields around Schwarzschild black holes by examining their quasinormal modes, revealing the existence of long-lived quasi-resonant modes and asymptotic frequency behavior.

Contribution

It demonstrates the conditions for quasi-resonant modes in massive scalar fields and analytically and numerically shows their frequency spectrum approaches a universal value.

Findings

Quasi-resonant modes exist only if the effective potential is non-zero at the boundaries.

The real part of the quasinormal frequencies approaches ln(3)/(8πM) as mode number n increases.

Long-lived modes can occur for massive scalar fields in Schwarzschild backgrounds.

Abstract

The decay of massive scalar field in the Schwarzschild black hole background is investigated here by consideration its quasinormal spectrum. It has been proved that the so-called $quasi-resonant$ modes, which are arbitrary long living (purely real) modes, can exist only if the effective potential is not zero at least at one of the boundaries of the $R$-region. We have observed that the quasinormal spectrum exists for all field masses and proved both analytically and numerically that when $n \to \infty$ the real part of the frequencies approaches the same asymptotical value ($\ln3/(8\pi M)$) as in the case of the massless field.