Revisiting black holes and their thermodynamics in Einstein-Kalb-Ramond gravity

TL;DR

The paper addresses black holes in Einstein-Kalb-Ramond gravity, where a rank-two KR field nonminimally couples to gravity and can trigger spontaneous Lorentz symmetry breaking. By enforcing KR field EOM consistency and employing the Wald covariant phase-space formalism, the authors derive two classes of exact static, higher-dimensional black-hole solutions with and without a cosmological constant, and compute the Noether mass and Wald entropy to establish the first law and Smarr relations. They show that the Noether mass differs from the Komar mass used in prior work, with implications for observational constraints on Lorentz violation, illustrated via Solar System tests like Mercury’s perihelion precession. The results generalize to nonzero $\Lambda$, yielding two branches with explicit thermodynamics, and provide a robust framework to test spontaneous Lorentz symmetry breaking in modified gravity through strong-field and cosmological settings.

Abstract

Einstein-Kalb-Ramond gravity is an alternative theory of gravity in which a rank-two antisymmetric tensor field, known as the Kalb-Ramond field, is nonminimally coupled to gravity and can induce spontaneous Lorentz symmetry breaking when it acquires a nonzero vacuum expectation value. In this work, we revisit Einstein-Kalb-Ramond gravity and obtain two classes of exact static black hole solutions with general topological horizons in diverse dimensions within this framework, both with and without a cosmological constant. We further analyze their thermodynamic properties and employ the Wald formalism to compute the Noether mass and entropy, thereby establishing the corresponding first law of black hole thermodynamics. Finally, we discuss the implications of the Noether mass charge for constraining spontaneous Lorentz symmetry breaking within the framework of Einstein-Kalb-Ramond gravity.