Scalar field perturbations of the Schwarzschild black hole in the G\"{o}del Universe

TL;DR

This study examines how scalar field perturbations behave around a Schwarzschild black hole in a G"{o}del Universe, revealing stability and how oscillation frequencies are affected by the universe's rotation.

Contribution

It provides the first analysis of scalar perturbations in a Schwarzschild-G"{o}del spacetime, including an analytical approximation for large multipole numbers.

Findings

Oscillation frequency decreases linearly with the G"{o}del scale parameter j.

Damping time increases as j increases.

The spacetime remains stable under scalar perturbations.

Abstract

We investigate the scalar field perturbations of the 4+1-dimensional Schwarzschild black hole immersed in a G\"{o}del Universe, described by the Gimon-Hashimoto solution.This may model the influence of the possible rotation of the Universe upon the radiative processes near a black hole. In the regime when the scale parameter $j$ of the G\"{o}del background is small, the oscillation frequency is linearly decreasing with $j$, while the damping time is increasing. The quasinormal modes are damping, implying stability of the Schwarzschild-G\"{o}del space-time against scalar field perturbations. The approximate analytical formula for large multipole numbers is found.