Static neutral black holes in Kalb-Ramond gravity

The Kalb-Ramond (KR) gravity theory, a modified gravity theory that nonminimally couples a KR field with a nonzero vacuum expectation value for the gravitational field, can spontaneously break the Lorentz symmetry of gravity. In a recent work, Yang et al. [Phys. Rev. D 108, 124004 (2023)] successfully derived Schwarzschild-like black hole solutions both with and without a nonzero cosmological constant within the framework of KR gravity. However, their analysis did not address the more general case of static, neutral, spherically symmetric black holes. In this paper, we fill this gap by resolving the field equations to construct more general static, neutral, spherically symmetric black hole solutions both with and without a nonzero cosmological constant. Our black hole solutions are shown to obey the first law and the Bekenstein-Smarr mass formulas of black hole thermodynamics. Moreover, we demonstrate that our static neutral spherically symmetric AdS black hole does not always satisfy the reverse isoperimetric inequality (RII), as the isoperimetric ratio can be larger or smaller than unity depending on the placement of the solution parameters within the parameter space. This behavior contrasts with the above-mentioned Schwarzschild-like AdS black hole in the KR gravity theory, which always obeys the RII. Significantly, the present more general static, neutral, spherically symmetric AdS black hole is the first example of a static AdS black hole that can violate the RII.