Quasinormal Modes and GUP-Corrected Hawking Radiation of BTZ Black Holes within Modified Gravity Frameworks

TL;DR

This paper investigates how modified gravity theories and the generalized uncertainty principle affect the quasinormal modes, effective potentials, and thermodynamics of BTZ black holes, with implications for black hole stability and gravitational wave detection.

Contribution

It provides a detailed analysis of QNMs and effective potentials of BTZ black holes within $f( ext{R})$ and Ricci-Inverse gravity frameworks, including GUP effects on black hole radiation.

Findings

Increased mass and parameters raise the potential barrier, indicating stronger confinement.

GUP modifies Hawking radiation, affecting QNM decay rates.

Modified gravity parameters significantly influence QNM frequencies and stability.

Abstract

This paper aims to explore the quasinormal modes (QNMs) and effective potential profiles of massless and rotating BTZ black holes within the frameworks of $f(\mathcal{R})$ and Ricci-Inverse ($\mathcal{RI}$) modified gravity theories, which, while producing similar space-time structures, exhibit variations due to distinct cosmological constants, $\Lambda_m$. We derive wave equations for these black hole perturbations and analyze the behavior of the effective potential $V_{\text{eff}}(r)$ under different values of mass $m$, cosmological constant $\Lambda_m$, and modified gravity parameters $\alpha_1$, $\alpha_2$, $\beta_1$, $\beta_2$, and $\gamma$. The findings indicate that increasing mass and parameter values results in a raised potential barrier, implying stronger confinement of perturbations and impacting black hole stability. Incorporating the generalized uncertainty principle, we also study its effect on the thermodynamics of rotating BTZ black holes, demonstrating how GUP modifies black hole radiation, potentially observable in QNM decay rates. Additionally, we investigate the motion of particles through null and timelike geodesics in static BTZ space-time, observing asymptotic behaviors for null geodesics and parameter-dependent shifts in potential for timelike paths. The study concludes that modified gravity parameters significantly influence QNM frequencies and effective potential profiles, offering insights into black hole stability and suggesting that these theoretical predictions may be tested through gravitational wave observations.