Scalar Quasi-Normal Modes of a Loop Quantum Black Hole

Abstract

We compute the Quasi-Normal Mode (QNM) frequencies for scalar perturbations for modified Schwarzschild black holes in Loop Quantum Gravity. We study the singularity-free polymerized metric characterised by two parameters encoding loop quantum effects: the minimal area gap $a_0$ and the polymeric deformation parameter $P$. We perform numerical computations using Leaver's continued fraction method and compare our results to other semi-analytical methods and existing literature. We study the effects on the QNM spectrum of variation of both deformation parameters and systematically compare to the standard Schwarzschild case. In particular we find that the scalar fundamental mode is modified from the third decimal for values of $P$ in accordance with the most recent astrophysical constraints. We also show that qualitative differences arise for highly damped modes: on the one hand, a new crossing of the imaginary axis occurs for high values of $a_0$ and, on the other hand, increasing $P$ produces a positive shift of the real part and an increase of the spacing in imaginary part between modes.

29 pages; auxiliary mathematica notebook QNM_recursion_coefficients.nb with explicit QNM recursion relation coefficients

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