Particle motion and thermal effects around a Kalb–Ramond black hole

Abstract This work is devoted to examining particle dynamics and thermodynamic behavior of a black hole in the framework of Kalb–Ramond gravity, framing the investigation through the lens of the optical–mechanical analogy. Within this context, we derive a generalized modified dispersion relation, which inherently depends on the underlying spacetime geometry through its metric components. The analysis begins by exploring some physical quantities influenced by the geometry, including the effective index of refraction, the group velocity, and the time delay experienced by particle modes. We then investigate the interparticle potential, considering both massive and massless cases. The thermodynamic properties of the system are subsequently addressed using ensemble theory. In this treatment, we compute the pressure, internal energy, entropy, and heat capacity across three distinct regions: in the immediate vicinity of the event horizon, at the photon sphere, and in the asymptotic region. Notably, all calculations presented throughout this paper admit closed-form analytical solutions.