Branch structure and nonextensive thermodynamics of Kalb-Ramond-ModMax black holes: observational signatures

TL;DR

This paper explores the properties, thermodynamics, and observational signatures of Kalb-Ramond-ModMax black holes, revealing branch-dependent behaviors and potential astrophysical signatures through lensing and photon propagation analyses.

Contribution

It introduces a novel black hole solution incorporating Kalb-Ramond and ModMax fields, analyzes its thermodynamics within a non-extensive framework, and identifies observable differences between solution branches.

Findings

Ordinary branch admits extremal and non-extremal black holes.

Phantom branch generally supports single-horizon geometries.

Lensing and photon propagation show distinct signatures for different branches.

Abstract

We investigate a static, spherically symmetric black hole arising in Einstein gravity coupled to a Kalb-Ramond field and ModMax nonlinear electrodynamics, both of which are independently well motivated extensions of standard electrovacuum gravity. The solution depends, beyond mass and charge, on a Lorentz-violating parameter, a ModMax deformation parameter, and a discrete branch selector $\zeta=\pm1$. We show that the ordinary branch admits extremal and non-extremal configurations, while the phantom branch generically supports a single-horizon geometry. Black-hole thermodynamics is analyzed within the Tsallis non-extensive framework, revealing branch-dependent stability and Joule-Thomson behavior. Weak gravitational lensing is analyzed using the Ono-Ishihara-Asada extension of the Gauss-Bonnet theorem, which is required by the non-Euclidean asymptotic structure of the Kalb-Ramond optical geometry and yields a negative topological correction that reduces light bending relative to the Schwarzschild baseline. Photon propagation in plasma and tidal forces are also studied, revealing clear optical and strong-field signatures that distinguish the two branches.