Particle Dynamics, Shadow and Hawking Sparsity of a Kalb-Ramond Black Hole Coupled to Nonlinear Electrodynamics

TL;DR

This paper investigates the properties of a Kalb-Ramond black hole coupled to nonlinear electrodynamics, analyzing geodesics, shadow, Hawking radiation, and observational constraints, revealing increased sparsity in Hawking radiation.

Contribution

It provides closed-form expressions for geodesic parameters, analyzes the shadow and quasinormal modes, and compares theoretical predictions with EHT observations, exploring the effects of KR fields and monopole charge.

Findings

Photon sphere and shadow analyzed and compared with EHT data.

Hawking sparsity parameter significantly increased due to KR field and monopole charge.

Photon ring remains consistent with observations across parameter space.

Abstract

We study the timelike and null geodesic structure of a static, spherically symmetric black hole sourced by a Kalb--Ramond (KR) field coupled to nonlinear electrodynamics (NED). The geometry is characterized by the mass $M$, the magnetic monopole charge $q$, and the Lorentz-violating parameters $(\gamma,\lambda)$. Closed-form expressions are derived for the effective potential, as well as the specific energy and angular momentum of massive particles on circular orbits. We further analyze the photon sphere, black hole shadow, and the Lyapunov exponent associated with unstable null circular geodesics. The latter determines the eikonal quasinormal-mode frequencies through $\omega_{\rm eik}=(\ell+1/2)\,\Omega_c-i(n+1/2)\,|\lambda_L|$. The shadow radius is compared with the Event Horizon Telescope (EHT) observations of M87$^\ast$ and Sgr~A$^\ast$, allowing us to identify the viable region in the $(q,\gamma)$ parameter space. Finally, we compute the Hawking temperature, horizon area, and the Gray--Visser sparsity parameter. We demonstrate that the combined effects of the KR field and magnetic monopole charge increase the sparsity parameter from the Schwarzschild value $16\pi^3 \simeq 496$ to nearly $1.7\times10^3$. This indicates a significantly sparser Hawking cascade compared to the Schwarzschild case, while the photon ring remains consistent with the EHT $1\sigma$ observational bounds across most of the physically allowed parameter range.