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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.01106 |
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| _version_ | 1866914422117629952 |
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| author | Rout, Abhishek Altschul, Brett |
| author_facet | Rout, Abhishek Altschul, Brett |
| contents | We study axial perturbations of Reissner-Nordström black holes within the general framework of parity-violating modified gravity theories. We derive the governing equations for a class of frame-dragging perturbations, focusing on the symmetry structure and radial dependence of the perturbed metric component, describing its behavior across three distinct regions: near the singularity ($r \rightarrow 0$), between the inner and outer Reissner-Nordström horizons ($r_-< r< r_+$), and in the asymptotic exterior regime ($r \rightarrow \infty$). Using a combination of analytical and numerical methods, we analyze the solutions for varying black hole charge-to-mass ratios ($Q/M$) and angular momentum parameters ($l$). Key findings include the suppression of perturbations by the electromagnetic field for higher $Q/M$; the emergence of radial resonance-like behavior for specific $l$ values; and a high degree of symmetry for solutions in the extremal limit ($Q/M \sim 1$), attributed to the AdS$_2 \times S^2$ near-horizon geometry. The WKB approximation is employed to study the high-$l$ regime, revealing quantized radial resonance modes and singular behavior in the extremal limit. Additionally, we explore the role of boundary conditions and the possibility of a Chern-Simons field $Θ$ as the source of the parity violation, showing that consistency and the behavior of the perturbations under time reversal demand a constant field (and thus no actually observable Chern-Simons effects) at leading order. These results provide a basis for further analysis of the stability and dynamical properties of charged black holes in parity-violating theories, with potential experimental signatures in gravitational wave observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First Order Axial Perturbation of the Reissner-Nordström Metric in a Possible Parity-Violating Gravity Background Rout, Abhishek Altschul, Brett General Relativity and Quantum Cosmology We study axial perturbations of Reissner-Nordström black holes within the general framework of parity-violating modified gravity theories. We derive the governing equations for a class of frame-dragging perturbations, focusing on the symmetry structure and radial dependence of the perturbed metric component, describing its behavior across three distinct regions: near the singularity ($r \rightarrow 0$), between the inner and outer Reissner-Nordström horizons ($r_-< r< r_+$), and in the asymptotic exterior regime ($r \rightarrow \infty$). Using a combination of analytical and numerical methods, we analyze the solutions for varying black hole charge-to-mass ratios ($Q/M$) and angular momentum parameters ($l$). Key findings include the suppression of perturbations by the electromagnetic field for higher $Q/M$; the emergence of radial resonance-like behavior for specific $l$ values; and a high degree of symmetry for solutions in the extremal limit ($Q/M \sim 1$), attributed to the AdS$_2 \times S^2$ near-horizon geometry. The WKB approximation is employed to study the high-$l$ regime, revealing quantized radial resonance modes and singular behavior in the extremal limit. Additionally, we explore the role of boundary conditions and the possibility of a Chern-Simons field $Θ$ as the source of the parity violation, showing that consistency and the behavior of the perturbations under time reversal demand a constant field (and thus no actually observable Chern-Simons effects) at leading order. These results provide a basis for further analysis of the stability and dynamical properties of charged black holes in parity-violating theories, with potential experimental signatures in gravitational wave observations. |
| title | First Order Axial Perturbation of the Reissner-Nordström Metric in a Possible Parity-Violating Gravity Background |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.01106 |