Thermodynamic topology of topological charged dilatonic black holes

Thermodynamic topology of topological charged dilatonic black holes

25 Nov 2024 | B. Hazarika1a, B. Eslam Panah2 b, and P. Phukon1,3c
This paper explores the thermodynamic topology of topological charged dilatonic black holes, focusing on the impact of the topological constant \( k \) on the event horizon and the thermodynamic properties of these black holes. The study begins by examining the characteristics of topological charged black holes in dilaton gravity, particularly the influence of the topological constant \( k \) on the event horizon. The thermodynamic and conserved quantities of these black holes are analyzed to ensure they satisfy the first law of thermodynamics. The thermodynamic topology is investigated by treating the black holes as thermodynamic defects and using the off-shell free energy method. This involves calculating winding numbers associated with these defects to categorize black holes based on their topological charge. The paper explores two types of thermodynamic ensembles: the fixed charge ensemble and the fixed potential ensemble. For each ensemble, the study examines different curvature hypersurfaces (elliptic, hyperbolic, and flat) and varies the parameters of dilaton gravity to understand how they affect the thermodynamic topology. Key findings include: - The topological charge of topological charged dilatonic black holes depends on the sign of the cosmological constant \( \Lambda \) and the value of the dilaton coupling parameter \( \alpha \). - For elliptic curvature hypersurfaces, the topological charge can be either +1 or 0, depending on the sign of \( \Lambda \) and \( \alpha \). - For hyperbolic and flat curvature hypersurfaces, the topological charge is always +1, with the topological class depending on the sign of \( \Lambda \) and \( \alpha \). - The topological charge remains invariant with variations in most thermodynamic parameters, except for \( \alpha \) and \( \Lambda \). The study provides insights into the structural properties of topological charged dilatonic black holes and highlights the differences in thermodynamic topology compared to charged black holes in General Relativity.This paper explores the thermodynamic topology of topological charged dilatonic black holes, focusing on the impact of the topological constant \( k \) on the event horizon and the thermodynamic properties of these black holes. The study begins by examining the characteristics of topological charged black holes in dilaton gravity, particularly the influence of the topological constant \( k \) on the event horizon. The thermodynamic and conserved quantities of these black holes are analyzed to ensure they satisfy the first law of thermodynamics. The thermodynamic topology is investigated by treating the black holes as thermodynamic defects and using the off-shell free energy method. This involves calculating winding numbers associated with these defects to categorize black holes based on their topological charge. The paper explores two types of thermodynamic ensembles: the fixed charge ensemble and the fixed potential ensemble. For each ensemble, the study examines different curvature hypersurfaces (elliptic, hyperbolic, and flat) and varies the parameters of dilaton gravity to understand how they affect the thermodynamic topology. Key findings include: - The topological charge of topological charged dilatonic black holes depends on the sign of the cosmological constant \( \Lambda \) and the value of the dilaton coupling parameter \( \alpha \). - For elliptic curvature hypersurfaces, the topological charge can be either +1 or 0, depending on the sign of \( \Lambda \) and \( \alpha \). - For hyperbolic and flat curvature hypersurfaces, the topological charge is always +1, with the topological class depending on the sign of \( \Lambda \) and \( \alpha \). - The topological charge remains invariant with variations in most thermodynamic parameters, except for \( \alpha \) and \( \Lambda \). The study provides insights into the structural properties of topological charged dilatonic black holes and highlights the differences in thermodynamic topology compared to charged black holes in General Relativity.
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