Dyonic ModMax Black Holes in Kalb-Ramond gravity with a Cloud of Strings as Source

TL;DR

This paper explores the properties of dyonic ModMax black holes in Kalb-Ramond gravity with a string cloud, analyzing their geodesics, shadows, thermodynamics, and radiation, revealing unique observational features.

Contribution

It provides the first analytic expressions for photon spheres, shadows, and thermodynamic relations for this complex black hole model, highlighting novel phenomenological implications.

Findings

Shadow size depends on asymptotics and ModMax charge screening.

Identifies a Hawking-Page-type phase transition in specific heat.

Spectral emission rate is governed by shadow radius.

Abstract

We investigate the geodesic structure, shadow, thermodynamics, and Hawking radiation from a dyonic ModMax black hole in Kalb-Ramond gravity with a cloud of strings. The combined presence of ModMax nonlinear electrodynamics, the Lorentz-violating Kalb-Ramond background, and the string cloud breaks asymptotic flatness and introduces a global conical deficit that modifies all observables through a single geometric prefactor. We derive analytic expressions for the photon sphere, critical impact parameter, and shadow radius, and show that the shadow size depends on both the non-flat asymptotics and the ModMax screening of the dyonic charge. For massive test particles, we determine the innermost stable circular orbit and the accretion efficiency as functions of all model parameters. We also establish the first law of black hole thermodynamics and the generalized Smarr relation for this solution, identify a Hawking-Page-type phase transition in the specific heat, and compute the spectral energy emission rate, which we show is directly governed by the shadow radius in the geometric-optics limit. Our results demonstrate that the interplay of these three ingredients produces a phenomenology observationally distinguishable from standard Reissner-Nordstr\"{o}m black holes.