Study of Null Geodesics and their Stability in Kalb-Ramond Black Holes
Abstract
We investigate null geodesics and their stability in four-dimensional charged Kalb-Ramond black holes with a cosmological constant. The non-vanishing vacuum expectation value of the background antisymmetric tensor field induces spontaneous Lorentz symmetry breaking, controlled by a dimensionless parameter l, and deforms the Reissner-Nordström-(A)dS geometry. We derive the effective potential for massless particles and obtain analytic expressions for the photon-sphere radius, critical impact parameter, capture cross section, and deflection trajectories. The limiting cases l→0 recover the RN, RN-dS and RN-AdS geodesic structures, while finite values of l shift the turning points, modify the bending of light and deform both first-kind and second-kind photon trajectories. In the AdS branch, we find a special limiting limaçon-type null geodesic whose angular structure is modified by the Kalb-Ramond parameter. We also compute the Lyapunov exponent of the unstable circular null orbit and show that the cosmological constant changes the instability timescale, whereas the Lorentz-violating parameter produces a non-trivial deformation of the photon-sphere instability. Our results identify null geodesics as sensitive probes of Lorentz-violating effects in charged black hole spacetimes.
Related
- Quasinormal modes, complex null geodesics and singularity resolution in regular AdS black holes
- Dyonic black holes in Lorentz-violating gravity with a background Kalb-Ramond field: Quasiperiodic oscillations and radiative properties
- Null Geodesics in the Reissner-Nordström Black Hole Spacetime Pierced by a Cosmic String
- Dyonic Black Holes in Lorentz-Violating Gravity with a Background Kalb--Ramond Field
- Probing Nonlinear Logarithmic Kalb-Ramond Black Holes: Particle Dynamics, Epicyclic Oscillations and Thermodynamic Signatures
BibTeX
@misc{gonzalez2026study,
title = {{Study of Null Geodesics and their Stability in Kalb-Ramond Black Holes}},
author = {P. A. González and Marco Olivares and Eleftherios Papantonopoulos and Yerko Vásquez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16471},
eprint = {2609.16471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16471},
}
RIS
TY - UNPB
TI - Study of Null Geodesics and their Stability in Kalb-Ramond Black Holes
AU - P. A. González
AU - Marco Olivares
AU - Eleftherios Papantonopoulos
AU - Yerko Vásquez
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16471
UR - https://arxiv.org/abs/2609.16471
AB - We investigate null geodesics and their stability in four-dimensional charged Kalb-Ramond black holes with a cosmological constant. The non-vanishing vacuum expectation value of the background antisymmetric tensor field induces spontaneous Lorentz symmetry breaking, controlled by a dimensionless parameter l, and deforms the Reissner-Nordström-(A)dS geometry. We derive the effective potential for massless particles and obtain analytic expressions for the photon-sphere radius, critical impact parameter, capture cross section, and deflection trajectories. The limiting cases l→0 recover the RN, RN-dS and RN-AdS geodesic structures, while finite values of l shift the turning points, modify the bending of light and deform both first-kind and second-kind photon trajectories. In the AdS branch, we find a special limiting limaçon-type null geodesic whose angular structure is modified by the Kalb-Ramond parameter. We also compute the Lyapunov exponent of the unstable circular null orbit and show that the cosmological constant changes the instability timescale, whereas the Lorentz-violating parameter produces a non-trivial deformation of the photon-sphere instability. Our results identify null geodesics as sensitive probes of Lorentz-violating effects in charged black hole spacetimes.
ER -