Abstract In this work, we study the thermodynamic topology of a static, a charged static, and a charged rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: the fixed charge (q) ensemble and fixed potential (ϕ) ensemble. For charged rotating black holes, four different types of ensembles are considered: fixed (q, J), fixed (ϕ, J), fixed (q, Ω), and fixed (ϕ, Ω) ensemble, where J and Ω denote the angular momentum and the angular frequency, respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topologies of these black holes via the computation of winding numbers at these defects. For the static black hole we work in three models. We find that the topological charge for a static black hole is always −1 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed ϕ ensemble, the topological charge is found to be −1. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged rotating black holes, in the fixed (q, J) ensemble, the topological charge is found to be 1. In the fixed (ϕ, J) ensemble, we find the topological charge to be 1. In the case of the fixed (q, Ω) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature (R). In the fixed (Ω, ϕ) ensemble, the topological charge is −1, 0, or 1 depending on the values of R, Ω, and ϕ. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters.
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"title": "Thermodynamic Topology of Black Holes in f(R) Gravity Nobel Lecture: Accelerating Expansion of the Universe through Observation of Distant Supernovae RPS thermodynamics of Taub\u2013NUT AdS black holes in the presence of central charge and the weak gravity conjecture Topological Interpretation of Black Hole Phase Transition in Gauss-Bonnet Gravity Thermodynamic Topological Classifications of Well-Known Black Holes Topology of black hole thermodynamics via R\u00e9nyi statistics R\u00e9nyi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions Topology and phase transition for EPYM AdS black hole in thermal potential Thermodynamic phase transition and winding number for the third-order Lovelock black hole Topology of critical points in boundary matrix duals Topological classes of BTZ black holes Thermodynamic Topology of D=4,5 Horava Lifshitz Black Hole in Two Ensembles Thermodynamic topology of Kerr-Sen black holes via R\u00e9nyi statistics The structure of the topological current Propagation and Fluxes of Ultra High Energy Cosmic Rays in f(R) Gravity Theory Anisotropies of Diffusive Ultra-high Energy Cosmic Rays in f(R) Gravity Theory"
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"value": "Abstract In this work, we study the thermodynamic topology of a static, a charged static, and a charged rotating black hole in f(R) gravity. For charged static black holes, we work in two different ensembles: the fixed charge (q) ensemble and fixed potential (\u03d5) ensemble. For charged rotating black holes, four different types of ensembles are considered: fixed (q, J), fixed (\u03d5, J), fixed (q, \u03a9), and fixed (\u03d5, \u03a9) ensemble, where J and \u03a9 denote the angular momentum and the angular frequency, respectively. Using the generalized off-shell free energy method, where the black holes are treated as topological defects in their thermodynamic spaces, we investigate the local and global topologies of these black holes via the computation of winding numbers at these defects. For the static black hole we work in three models. We find that the topological charge for a static black hole is always \u22121 regardless of the values of the thermodynamic parameters and the choice of f(R) model. For a charged static black hole, in the fixed charge ensemble, the topological charge is found to be zero. Contrastingly, in the fixed \u03d5 ensemble, the topological charge is found to be \u22121. For charged static black holes, in both the ensembles, the topological charge is observed to be independent of the thermodynamic parameters. For charged rotating black holes, in the fixed (q, J) ensemble, the topological charge is found to be 1. In the fixed (\u03d5, J) ensemble, we find the topological charge to be 1. In the case of the fixed (q, \u03a9) ensemble, the topological charge is 1 or 0 depending on the value of the scalar curvature (R). In the fixed (\u03a9, \u03d5) ensemble, the topological charge is \u22121, 0, or 1 depending on the values of R, \u03a9, and \u03d5. Therefore, we conclude that the thermodynamic topologies of the charged static black hole and charged rotating black hole are influenced by the choice of ensemble. In addition, the thermodynamic topology of the charged rotating black hole also depends on the thermodynamic parameters."
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