Conformal Weyl gravity via two stages of quasinormal ringing and late-time behavior

TL;DR

This paper investigates the quasinormal ringing and late-time behavior of scalar and electromagnetic fields in conformal Weyl gravity black hole solutions, revealing three distinct evolution stages influenced by additional constants in the metric.

Contribution

It demonstrates how extra constants in conformal Weyl gravity alter the quasinormal ringing and late-time tail behaviors of fields around black holes, highlighting new dynamical features.

Findings

Scalar field evolution exhibits three stages: Schwarzschild-like ringing, dark matter ringing, and de Sitter exponential tail.

Electromagnetic field tails appear even without the effective de Sitter constant.

The effective dark matter term significantly changes the asymptotic behavior of field evolution.

Abstract

Black hole (BH) solution in the conformal Weyl gravity is a generalization of the Schwarzschild spacetime which includes two additional constants appearing when integrating the third order differential equations for gravitational field. One constant looks like the effective cosmological constant providing the de Sitter asymptotic of the solution. The other constant allows one to describe flat rotation of galaxies without introducing of the dark matter. Here we show that the effective "dark matter" term in the metric function drastically changes the asymptotic behavior of the evolution of the wave function of a scalar field: after the Schwarzschild-like ringing phase, the ringing at another, non-Schwarzschildian, longer-lived frequency takes place before the beginning of the exponential asymptotic tail. Thus the evolution of the scalar field consists of the three qualitatively different stages: the Schwarzschild-like ringing phase, the effective dark matter ringing phase and the de Sitter phase characterized by exponential tails. The late time behavior of the electromagnetic field is qualitatively different as well: the exponential tails appear even in the absence of the effective de Sitter term.