The ringing of quantum corrected Schwarzschild black hole with GUP

TL;DR

This paper investigates how quantum corrections based on the generalized uncertainty principle (GUP) affect Schwarzschild black holes, focusing on quasinormal modes and potential functions, revealing differences between scalar and electromagnetic perturbations.

Contribution

It introduces quantum corrections via GUP into Schwarzschild black holes and analyzes their impact on quasinormal modes using the sixth-order WKB method.

Findings

Quantum corrections alter the black hole potential and QNM frequencies.

Scalar field perturbations have larger potentials and QNM frequencies than electromagnetic ones.

The GUP parameter influences the discretization and structure of black hole spacetime.

Abstract

Schwarzschild black holes with quantum corrections are studied under scalar field perturbations and electromagnetic field perturbations to analyze the effect of the correction term on the potential function and quasinormal mode (QNM). In classical general relativity, spacetime is continuous and there is no existence of the so-called minimal length. The introduction of the correction items of the generalized uncertainty principle (GUP), the parameter $\beta$, can change the singularity structure of the black hole gauge and may lead to discretization in time and space. We apply the sixth-order WKB method to approximate the QNM of Schwarzschild black holes with quantum corrections and perform numerical analysis to derive the results of the method. Also, we find that the effective potential and QNM in scalar fields are larger than those in electromagnetic fields.