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

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 ($\mathcal{R}\mathcal{I}$) 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.

28 pages and 10 Figures

References in corpus (16)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Modified theories of Gravity: Why, How and What?
• Testing Rotating Regular Metrics as Candidates for Astrophysical Black Holes
• Topical Review: Greybody Factors and Quasinormal Modes for Black Holes in Various Theories -- Fingerprints of Invisibles
• Ergosphere and shadow of a rotating regular black hole
• Noncommutative Schwarzschild black hole surrounded by quintessence: Thermodynamics, Shadows and Quasinormal modes
• Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings
• Quasinormal Modes and Phase Structure of Regular $AdS$ Einstein-Gauss-Bonnet Black Holes
• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• GUP-corrected black holes: Thermodynamic properties, evaporation time and shadow constraint from EHT Observations of M87* and Sgr A*
• Weak Deflection Angle, Greybody Bound and Shadow for Charged Massive BTZ Black Hole
• Stationary BTZ space-time in Ricci-Inverse and $f(\mathcal{R})$ gravity theories
• Time-Machines Construct in $f(\mathcal{R},\mathcal{A},A^{\mu \nu }{A}_{\mu \nu })$ and $f(\mathcal{R})$ Modified Gravity Theories
• Can the induced increase in the angular velocity prevent the overspinning of BTZ black holes?
• Hawking radiation at the zero temperature limit

Cited by in corpus (3)

• AdS Black String in a Cosmic Web: Geodesics, Shadows, and Thermodynamics
• Traversable Wormholes in Einstein-Euler-Heisenberg Gravity: Geometry, Energy Conditions, and Gravitational Lensing
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy