Exact black hole solutions in Palatini Kalb-Ramond gravity
Abstract
We investigate static and spherically symmetric black holes in Palatini Kalb-Ramond gravity, where a nonzero vacuum expectation value of the Kalb-Ramond field spontaneously breaks local Lorentz symmetry. Treating the metric and the torsion-free affine connection as independent variables, we derive the modified field equations and obtain an exact family of solutions encompassing positive, vanishing, and negative values of the cosmological constant Λ. Unlike the corresponding purely metric formulation, the Palatini theory consistently allows both Lorentz-violating parameters ℓ1 and ℓ2 to be nonzero. Using the Iyer-Wald formalism, we determine the conserved mass of the black hole solutions. For the Λ≤0 sector, we further verify the first law and the Smarr relation, identifying the conserved mass as the thermodynamic enthalpy. We then confront the Λ=0 solution with Mercury's perihelion precession, solar light deflection, and the Shapiro time delay. Once the central mass parameter is calibrated by planetary dynamics, these observables constrain the Lorentz-violating parameters only through q≡ℓ2/(1−ℓ1). Among these tests, Mercury's perihelion precession yields the most stringent constraint, −7.4×10−12 ≤ q ≤ 3.7×10−11.
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BibTeX
@misc{she2026exact,
title = {{Exact black hole solutions in Palatini Kalb-Ramond gravity}},
author = {Lin-Yi She and Rui-Jie Niu and Ke Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05799},
eprint = {2610.05799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05799},
}
RIS
TY - UNPB
TI - Exact black hole solutions in Palatini Kalb-Ramond gravity
AU - Lin-Yi She
AU - Rui-Jie Niu
AU - Ke Yang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05799
UR - https://arxiv.org/abs/2610.05799
AB - We investigate static and spherically symmetric black holes in Palatini Kalb-Ramond gravity, where a nonzero vacuum expectation value of the Kalb-Ramond field spontaneously breaks local Lorentz symmetry. Treating the metric and the torsion-free affine connection as independent variables, we derive the modified field equations and obtain an exact family of solutions encompassing positive, vanishing, and negative values of the cosmological constant Λ. Unlike the corresponding purely metric formulation, the Palatini theory consistently allows both Lorentz-violating parameters ℓ_1 and ℓ_2 to be nonzero. Using the Iyer-Wald formalism, we determine the conserved mass of the black hole solutions. For the Λ≤0 sector, we further verify the first law and the Smarr relation, identifying the conserved mass as the thermodynamic enthalpy. We then confront the Λ=0 solution with Mercury's perihelion precession, solar light deflection, and the Shapiro time delay. Once the central mass parameter is calibrated by planetary dynamics, these observables constrain the Lorentz-violating parameters only through q≡ℓ_2/(1−ℓ_1). Among these tests, Mercury's perihelion precession yields the most stringent constraint, −7.4×10^−12 ≤ q ≤ 3.7×10^−11.
ER -