Static and spherically symmetric black holes in gravity with a background Kalb-Ramond field

The Lorentz symmetry of gravity is spontaneously broken when the nonminimally coupled Kalb-Ramond field acquires a nonzero vacuum expectation value. In this work, we present exact solutions for static and spherically symmetric black holes in the framework of this Lorentz-violating gravity theory. In order to explore the physical implications of Lorentz violation, we analyze the thermodynamic properties of the obtained solutions and evaluate the impact of Lorentz violation on some classical gravitational experiments within the Solar System. Furthermore, the Lorentz-violating parameter is constrained by using the measured results of these experiments.