Thermodynamic topology of black holes in F(R)-Euler–Heisenberg gravity’s Rainbow
Sekhmani Y. Gashti S.N. Afshar M.A.S. Alipour M.R. Sadeghi J. Pourhassan B. Maurya S.K. Rayimbaev J.
2025World Scientific
International Journal of Geometric Methods in Modern Physics
2025
The topology of black hole thermodynamics is a fascinating area of study that explores the connections between thermodynamic properties and topological features of black holes. It often involves analyzing critical points in the phase diagrams of black holes and assigning topological charges to these points. One significant approach is based on Duan’s topological current ϕ-mapping theory, which introduces the concept of topological charges to critical points in black hole thermodynamics. We successfully derive the field equations for F(R)-Euler–Heisenberg theory, providing a framework for studying the interplay between modified gravity and nonlinear electromagnetic effects. We obtain an analytical solution for a static, spherically symmetric, energy-dependent black hole with constant scalar curvature. Also, our analysis of black holes in F(R)-Euler–Heisenberg gravity’s Rainbow reveals significant insights into their topological properties. We identified the total topological charges by examining the normalized field lines along various free parameters. Our findings indicate that the parameters (R0) and (fE = gE) influence the topological charges. These results are comprehensively summarized in Tables. In examining the photon sphere within this model, the sign of the parameter R0 plays a crucial role in determining whether the model adopts a dS or AdS configuration. An interesting characteristic of this model is that, in its AdS form, it avoids the formation of naked singularity regions, which sets it apart from many other models. Typically, varying parameter values in other models can result in the division of space into regions of black holes and naked singularities. However, this model consistently retains its black hole behavior by featuring an unstable photon sphere, regardless of parameter values within the acceptable range. In its dS form, the behavior of the model’s photon sphere remains consistent with other dS models and does not exhibit unique differences.
F(R)-Euler–Heisenberg gravity’s Rainbow , photon sphere , Thermodynamic topology
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Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
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
School of Physics, Damghan University, P.O. Box 3671641167, Damghan, Iran
Department of Physics, University of Mazandaran, Faculty of Basic, Sciences, P.O. Box 47416-95447, Babolsar, Iran
Canadian Quantum Research Center, 204-3002 32 Ave, Vernon, V1T 2L7, BC, Canada
Centre of Research Impact and Outcome, Chitkara University, Punjab, Rajpura, 140417, 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
Center for Theoretical Physics
Institute of Nuclear Physics
Department of Mathematical and Physical Sciences
School of Physics
Department of Physics
Canadian Quantum Research Center
Centre of Research Impact and Outcome
Urgench State University
University of Tashkent for Applied Sciences
National University of Uzbekistan
Tashkent State Technical University
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