Kalb-Ramond black holes sourced by ModMax electrodynamics: Some perturbative properties in the phantom sector
Sekhmani Y. Baruah A. Maurya S.K. Rayimbaev J. Altanji M. Ibragimov I. Muminov S.
December 2025Elsevier B.V.
Physics of the Dark Universe
2025#50
We formulate and analyse 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 ℓ . To incorporate both the standard and phantom sectors, we introduce a discrete sign-flip parameter ζ = ± 1 that flips the gauge-kinetic terms in the phantom ( ζ = − 1 ) branch. Assuming a vanishing cosmological constant and 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–Nordström, and ModMax BHs, with curvature scalars showing deviations controlled by ( ℓ , γ , ζ ) . We study scalar, electromagnetic, and gravitational perturbations using both frequency-domain (Padé-averaged WKB) and time-domain (Gundlach–Price–Pullin ＋ Prony) methods. We find that increasing either ℓ or the ModMax parameter γ enhances the real and imaginary parts of quasinormal modes, 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 analyse the greybody factors and compute the sparsity η of Hawking radiation, which quantifies the non-thermal character of particle emission. We show that η is significantly affected by ℓ , decreasing with increasing Lorentz violation and asymptotically approaching a scaled version of the Schwarzschild value.
Black holes , Kalb-Ramond gravity , Perturbation analysis , QMNs
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Center for Theoretical Physics, Khazar University, 41 Mehseti Street, AZ, Baku, 1096, Azerbaijan
Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, Rajpura, 140401, India
Institute of Nuclear Physics, Ibragimova, 1, Almaty, 050032, Kazakhstan
Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, P.O. Box 33, Nizwa, 616, Oman
Department of Physics, Albert Einstein School of Physical Sciences, Assam University, Assam, Silchar, 788011, India
Urgench State University, Kh. Alimjan Str. 14, Urgench, 221100, Uzbekistan
University of Tashkent for Applied Sciences, Str. Gavhar 1, Tashkent, 100149, Uzbekistan
National University of Uzbekistan, Tashkent, 100174, Uzbekistan
Tashkent State Technical University, Tashkent, 100095, Uzbekistan
Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia
Kimyo International University in Tashkent, Shota Rustaveli street 156, Tashkent, 100121, Uzbekistan
Mamun University, Bolkhovuz Street 2, Khiva, 220900, Uzbekistan
Center for Theoretical Physics
Centre for Research Impact & Outcome
Institute of Nuclear Physics
Department of Mathematical and Physical Sciences
Department of Physics
Urgench State University
University of Tashkent for Applied Sciences
National University of Uzbekistan
Tashkent State Technical University
Department of Mathematics
Kimyo International University in Tashkent
Mamun University
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