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 (35)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• 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
• Shadow and stability of quantum-corrected black holes
• Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes
• Cosmological constant corrections to the photon sphere and black hole shadow radii
• Investigating the Connection between Generalized Uncertainty Principle and Asymptotically Safe Gravity in Black Hole Signatures through Shadow and Quasinormal Modes
• Topical Review: Greybody Factors and Quasinormal Modes for Black Holes in Various Theories -- Fingerprints of Invisibles
• Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Ergosphere and shadow of a rotating regular black hole
• Weak gravitational lensing and shadow of a GUP-modified Schwarzschild black hole in the presence of plasma
• Gravitational axial perturbations of Schwarzschild-like black holes in dark matter halos
• Ricci-inverse gravity: a novel alternative gravity, its flaws, and how to cure them
• Exponential corrected thermodynamics of Born-Infeld BTZ black holes in massive gravity
• 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
• Quasi-normal modes of non-separable perturbation equations: the scalar non-Kerr case
• Can we bypass no-go theorem for Ricci-inverse Gravity?
• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• Physical Properties of Brane-World Black Hole Solutions via a Confining Potential
• Quantum corrected thermodynamics of nonlinearly charged BTZ black holes in massive gravity's rainbow
• Quasinormal modes and stability of boosted Reissner-Nordström AdS black holes
• Cosmological constant Petrov type-N space-time in Ricci-inverse 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
• Quasinormal modes, Hawking radiation and absorption of the massless scalar field for Bardeen black hole surrounded by perfect fluid dark matter
• Scalar field instabilities in charged BTZ black holes
• 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