Exact static and slowly rotating phantom conformal nonlinear-electrodynamic black holes in Bumblebee gravity with Lorentz Violation and shadow phenomenology
Sekhmani Y. Maurya S.K. Rayimbaev J. Altanji M. Ibragimov I. Muminov S.
December 2025Elsevier B.V.
Physics of the Dark Universe
2025#50
We derive exact static and slowly rotating charged black hole solutions within the framework of Einstein-Bumblebee gravity coupled to phantom ModMax electrodynamics. In this context, the breaking of Lorentz symmetry is parameterized by ℓ , the nonlinear gauge self-coupling is represented by γ , and the phantom branch is denoted by ζ = ± 1 . The Lorentz-violating shift ℓ uniformly rescales the radial metric component, resulting in an asymptotically “tilted” vacuum. The ModMax parameter γ influences the Coulomb term through an exponential factor, e − γ . Additionally, the condition ζ = − 1 introduces a negative energy charge, which serves to enlarge the horizon and elevate the extremal spin bound. In the rotating extension, these couplings induce distinct shifts in the photon sphere and shadow: the parameter ℓ modifies the overall size, γ adjusts the lensing strength, and ζ alters the shape of the silhouette. Confronting our model with EHT observations of M87 ∗ , where θ d = 42 ± 3 , μ as , yields viable parameter bands in the ( a / M , Q / M ) plane. Specifically, we find that a / M ≳ 0 . 75 and Q / M ≲ 0 . 35 across the ( γ , ℓ ) = ± ( 0 . 1 , 0 . 05 ) corners. In the case of Sgr A ∗ , where the derived diameter is θ d = 50 ± 5 , μ as , the tighter silhouette constraints lead to the following conclusions: spins are restricted to the range a / M ≈ 0 . 40 – 0 . 75 , while charges must satisfy Q / M ≲ 0 . 25 . Additionally, this analysis necessitates that ℓ ≲ 0 . 05 and | γ | ≲ 0 . 1 within the phantom branch. This provides one of the strongest astrophysical constraints to date on Lorentz violation and nonlinear phantom electrodynamics.
Black holes , Lorentz symmetry breaking , M87* , ModMax , Phantom , Sgr A*
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Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
Centre for Research Impact & Outcome, Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, Rajpura, 140401, India
Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, P.O. Box 33, Nizwa, 616, Oman
Institute of Nuclear Physics, Ibragimova, 1, Almaty, 050032, Kazakhstan
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
Urgench State University, Kh. Alimjan Str. 14, Urgench, 221100, 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
Department of Mathematical and Physical Sciences
Institute of Nuclear Physics
University of Tashkent for Applied Sciences
National University of Uzbekistan
Tashkent State Technical University
Urgench State University
Department of Mathematics
Kimyo International University in Tashkent
Mamun University
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