[Paper Review] Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes

Rajes Ghosh, Mostafizur Rahman+1 more|arXiv (Cornell University)|Sep 25, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates a phenomenological regularized stable Kerr black hole model with two additional parameters (b and e) to resolve singularities and mass inflation instability. It analyzes scalar quasi-normal modes for stability and compares shadow sizes with Event Horizon Telescope observations, finding the model stable for all (b,e) and constraining e via EHT data while b remains unconstrained.

ABSTRACT

Black hole solutions in general relativity come with pathologies such as singularity and mass inflation instability, which are believed to be cured by a yet-to-be-found quantum theory of gravity. Without such consistent description, one may model theory-agnostic phenomenological black holes that bypass the aforesaid issues. These so-called regular black holes are extensively studied in the literature using parameterized modifications over the black hole solutions of general relativity. However, since there exist several ways to model such black holes, it is important to study the consistency and viability of these solutions from both theoretical and observational perspectives. In this work, we consider a recently proposed model of regularized stable rotating black holes having two extra parameters in addition to the mass and spin of a Kerr solution. We start by computing their quasi-normal modes under scalar perturbation and investigate the impact of those additional parameters on black hole stability. In the second part, we study the shadow structures of these regularized black holes and obtain stringent bounds on the parameter space requiring consistency with Event Horizon Telescope observations of $M87^*$ and $Sgr\, A^*$ shadows.

Motivation & Objective

• To assess the stability of a recently proposed regularized stable rotating black hole model with two extra parameters (b and e) against scalar perturbations.
• To test the viability of the model by comparing its predicted black hole shadow with Event Horizon Telescope (EHT) observations of M87* and Sgr A*.
• To constrain the parameter space of b and e using observational data, particularly focusing on deviations from the standard Kerr solution.
• To explore the implications of the model for cosmic censorship and the structure of spacetime near the black hole core.
• To provide the first observational bounds on the parameters of this regularized black hole model using QNM and shadow data.

Proposed method

• Computes scalar quasi-normal modes (QNMs) for the regularized stable Kerr black hole using the WKB approximation up to 6th order.
• Analyzes the imaginary part of QNM frequencies to determine stability: negative values indicate stable damping of perturbations.
• Derives null geodesics and computes the black hole shadow radius using the impact parameter method and photon sphere analysis.
• Compares the angular size of the shadow with EHT observations of M87* and Sgr A*, varying parameters b and e across different inclination angles.
• Uses contour plots to visualize shadow size variation and applies observational constraints from EHT data to bound the parameter space.
• Applies consistency checks on the mass profile m(r) to ensure physical viability and avoid violations of weak cosmic censorship.

Experimental results

Research questions

• RQ1 Is the regularized stable Kerr black hole model stable under scalar perturbations across its parameter space (b, e)?
• RQ2 How do the additional parameters b and e affect the quasi-normal mode spectrum and relaxation timescale of the black hole?
• RQ3 To what extent does the shadow size of the regularized black hole deviate from the Kerr solution, and can it be distinguished via EHT observations?
• RQ4 What are the observational bounds on the parameters b and e derived from consistency with EHT shadow measurements of M87* and Sgr A*?
• RQ5 Does the model satisfy physical consistency conditions such as weak cosmic censorship and regularity of the mass profile?

Key findings

• The regularized stable Kerr black hole is found to be stable under scalar perturbations for all allowed values of (b, e), as the imaginary parts of the QNM frequencies remain negative.
• For fixed e, increasing b leads to a decrease in the imaginary part of QNM frequencies, indicating enhanced stability and shorter relaxation times.
• In the e-extremal limit (e → 2), both real and imaginary parts of the QNM frequencies approach zero, signaling a critical transition point where stability is compromised.
• The parameter b, related to the conformal factor, does not affect null geodesics or shadow size, leaving the shadow radius unchanged regardless of b.
• The parameter e has a strong influence on the shadow size: values of e > 1.7 are ruled out by EHT observations of Sgr A*, while e ∈ (−6.341, 1.7] is allowed for inclination angles θ_i < 50°.
• The model allows for shadows consistent with EHT observations for M87* and Sgr A* within specific e-bounds, enabling distinction from the Kerr solution via QNM structure despite similar shadow morphology.