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Exact black hole solutions in gravity with a background Kalb-Ramond field (2505.07404v1)
Published 12 May 2025 in gr-qc
Abstract: In this work, we derive exact solutions for four-dimensional static spherically symmetric black holes and three-dimensional rotating black holes within a Lorentz-violating gravity theory. In this framework, Lorentz symmetry is spontaneously broken when a nonminimally coupled Kalb-Ramond tensor field acquires a nonzero vacuum expectation value. Building upon these solutions, we investigate the thermodynamic properties of the black holes using the Iyer-Wald formalism. Our findings reveal that the standard first law of thermodynamics and the Smarr relation remain valid for black holes in the presence of the Kalb-Ramond field.