Kalb-Ramond Black Holes Sourced by ModMax Electrodynamics: Some Perturbative Properties in the Phantom Sector

TL;DR

This paper introduces new charged black hole solutions in Lorentz-violating gravity with nonlinear electrodynamics, analyzing their perturbative properties and how Lorentz violation influences quasinormal modes, potentials, and Hawking radiation.

Contribution

It presents exact analytical black hole solutions with Lorentz violation and ModMax electrodynamics, and studies their perturbations and radiation characteristics.

Findings

Higher Lorentz violation increases QNM frequencies and damping.

Effective potentials become deeper with phantom deformation.

Greybody factors decrease as Lorentz violation grows.

Abstract

We formulate and analyze a new class of electrically charged black hole (BH) solutions in Lorentz-violating gravity, where nonlinear ModMax electrodynamics is nonminimally coupled to a Kalb-Ramond (KR) two-form field. The spontaneous breaking of local Lorentz symmetry is triggered by a nonzero vacuum expectation value of the KR field, characterized by a small dimensionless parameter $\ell$. To incorporate both standard and phantom sectors, we introduce a discrete sign-flip parameter $\zeta = \pm1$, which flips the gauge-kinetic terms in the phantom ($\zeta = -1$) branch. Assuming a vanishing cosmological constant and a self-interacting potential with minimum $V' = 0$, we obtain exact analytical solutions for the metric function and electric potential. The resulting spacetime interpolates between Schwarzschild, Reissner-Nordstrom, and ModMax BHs, with curvature scalars showing deviations controlled by $(\ell, \gamma, \zeta)$. We study scalar, electromagnetic, and gravitational perturbations using both frequency-domain (Pade-averaged WKB) and time-domain (Gundlach-Price-Pullin plus Prony) methods. We find that increasing either $\ell$ or the ModMax parameter $\gamma$ enhances the real and imaginary parts of QNMs, indicating higher oscillation frequencies and faster damping, especially in the phantom sector. The effective potentials deepen under phantom deformation, supporting more tightly bound modes. Furthermore, we analyze the greybody factors and compute the sparsity $\eta$ of Hawking radiation, which quantifies the nonthermal character of particle emission. We show that $\eta$ is significantly affected by $\ell$, decreasing with increasing Lorentz violation and asymptotically approaching a scaled version of the Schwarzschild value.