Shadow, quasinormal modes, greybody bounds, and Hawking sparsity of Loop Quantum Gravity motivated non-rotating black hole

TL;DR

This paper investigates the effects of Loop Quantum Gravity on non-rotating black holes, analyzing their shadows, quasinormal modes, Hawking radiation, and area spectrum, revealing quantum corrections influence various observable properties.

Contribution

It provides analytical expressions for black hole shadow radii, studies quasinormal modes and Hawking radiation with quantum corrections, and derives a distinct area spectrum for LQG-inspired black holes.

Findings

Shadow and photon sphere radii increase with LQG parameter lpha.

Quasinormal mode oscillation and decay rates decrease as lpha increases.

Hawking radiation sparsity is significantly affected by quantum corrections.

Abstract

We consider Loop Quantum Gravity(LQG) motivated $4D$ polymerized black hole and study shadow, quasinormal modes, and Hawking radiation. We obtain analytical expressions of photonsphere radius and shadow radius and study their qualitative and quantitative nature of variation with respect to the LQG parameter $\alpha$. We also show shadows of the black hole for various values of $\alpha$. Our study reveals that both radii increase with an increase in the parameter value. We, then, study quasinormal modes for scalar and electromagnetic perturbations using the $6th$ order WKB method. Our study reveals that the LQG parameter impacts quasinormal modes. We observe that the oscillation of gravitational wave(GW) and decay rate decrease as $\alpha$ increases. At the same time, the error associated with the $6th$ order WKB method increases with an increase in $\alpha$. The ringdown waveform for electromagnetic and scalar perturbations is shown. We also study greybody bounds, power spectrum, and sparsity of Hawking radiation. Greybody bounds for electromagnetic perturbations do not depend on $\alpha$. For scalar perturbation, greybody bounds increase as the LQG parameter increases, but the variation with $\alpha$ is very small. The peak of the power spectrum as well as total power emitted decrease as we increase the value of $\alpha$. Also, the sparsity of Hawking radiation gets significantly impacted by quantum correction. Finally, we obtain the area spectrum of the black hole. It is found to be significantly different than that for the Schwarzschild black hole.