Scalar, Vector Perturbations and Effective Hawking Radiation of Cylindrical Black Holes in $f(\mathcal{R})$ and Ricci-Inverse Gravity

TL;DR

This paper explores scalar and vector perturbations, quasinormal modes, and Hawking radiation modifications of cylindrical black holes within $f( ext{R})$ and Ricci-Inverse gravity, revealing quantum and stability effects in these extended theories.

Contribution

It introduces a comprehensive analysis of black hole perturbations, thermodynamics, and quantum corrections in $f( ext{R})$ and Ricci-Inverse gravity, extending understanding beyond classical general relativity.

Findings

Modified quasinormal modes depend on gravity parameters.

GUP leads to significant deviations in Hawking temperature and entropy.

Black hole stability is influenced by higher-order curvature terms.

Abstract

This paper investigates scalar perturbations and quasinormal modes (QNMs) associated with cylindrical black holes constructed within the frameworks of $f(\mathcal{R})$-gravity and Ricci-Inverse ($\mathcal{RI}$) gravity. Moreover, we study the modified Hawking radiation in these black hole solutions and analyze the effects of coupling constants. These modified theories, which extend general relativity by introducing higher-order curvature corrections and additional geometric terms, provide a rich platform for exploring deviations from standard gravitational physics. The study begins by revisiting the cylindrical black holes in these modified gravity theories, where the effective cosmological constants respectively, are represented by $\Lambda_m^{f(\mathcal{R})}$ and $\Lambda_m^{\mathcal{RI}}$ related to the coupling constants unique to each framework. Afterwards, the QNMs, intrinsic damped oscillations of the black hole space-time, are analyzed to probe the stability of the system, with the effective potential $V$ revealing the impact of the modified gravity parameters. Additionally, the thermodynamic properties of the black holes are examined through the lens of the Generalized Uncertainty Principle (GUP), which introduces quantum corrections to Hawking radiation. The GUP-modified Hawking temperature and entropy are derived, demonstrating significant deviations from classical results and highlighting the quantum gravitational effects in these modified frameworks. By linking QNMs, thermodynamics, and quantum corrections, this work not only deepens the understanding of modified gravity theories but also offers potential observational pathways to test their validity.