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Thermodynamic topology of Black Holes in $F(R)$-Euler-Heisenberg gravity's Rainbow

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arxiv 2409.04997 v2 pith:PI5DZE3Z submitted 2024-09-08 gr-qc hep-th

classification gr-qchep-th
keywords blackmodelholestopologicaleuler-heisenberggravityholemodels
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abstract

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. We successfully derive the field equations for $F(R)$-Euler-Heisenberg theory, providing a framework for studying the interplay between modified gravity and non-linear 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 $( R_0 )$ and $( f_{\epsilon} = g_{\epsilon} )$ influence the topological charges. These results are comprehensively summarized in Table I. In examining the photon sphere within this model, the sign of the parameter \( R_0 \) 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.

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Cited by 10 Pith papers

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    For noncommutative RN-AdS black holes, the paper claims bulk and boundary thermodynamic topological charges equal to zero and derives perturbative second-law corrections to the remnant-mass bound.

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  7. Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids

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  10. Topological Insights into Black Hole Thermodynamics: Non-Extensive Entropy in CFT framework

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