Thermodynamic topology of topological charged dilatonic black holes

Thermodynamic topology of topological charged dilatonic black holes

25 Nov 2024 | B. Hazarika, B. Eslam Panah, P. Phukon
This paper explores the thermodynamic topology of topological charged dilatonic black holes in dilaton gravity. The study begins by examining the characteristics of these black holes, focusing on the impact of the topological constant on their event horizons. The thermodynamic and conserved quantities of these black holes are analyzed to assess the validity of the first law of thermodynamics. The black holes are treated as thermodynamic defects, and two statistical ensembles—fixed charge (q) and fixed potential (φ)—are considered to study the effects of the topological constant (k) on thermodynamic topology. The analysis involves calculating the topological charges at the defects within their thermodynamic spaces, examining both local and global topology, and investigating how dilaton gravity parameters affect the thermodynamic topology of black holes compared to charged black holes in General Relativity. The paper derives the solution for topological charged black holes in dilaton gravity, discusses their thermodynamic properties, and explores the concept of thermodynamic topology. The thermodynamic topology is analyzed using the off-shell free energy method, which views black holes as topological defects. The study identifies the winding numbers associated with these defects, which classify black holes into different topological classes. The topological charge is calculated using Duan's φ-mapping technique, and the results show that the topological charge depends on the value of the topological constant (k) and the parameters of dilaton gravity. In the fixed charge ensemble, the topological charge is found to be zero for positive values of the cosmological constant (Λ) and either zero or one for negative values of Λ, depending on the value of α. In the fixed potential ensemble, the topological charge is found to be -1 for positive Λ and varies with the sign of Λ and other parameters. The study also highlights the differences in thermodynamic topology between charged black holes in dilaton gravity and those in General Relativity. The results show that the topological charge is influenced by the curvature of the hypersurface (k), the parameters of dilaton gravity, and the sign of the cosmological constant. The findings provide insights into the structural properties of black holes within the framework of thermodynamic topology.This paper explores the thermodynamic topology of topological charged dilatonic black holes in dilaton gravity. The study begins by examining the characteristics of these black holes, focusing on the impact of the topological constant on their event horizons. The thermodynamic and conserved quantities of these black holes are analyzed to assess the validity of the first law of thermodynamics. The black holes are treated as thermodynamic defects, and two statistical ensembles—fixed charge (q) and fixed potential (φ)—are considered to study the effects of the topological constant (k) on thermodynamic topology. The analysis involves calculating the topological charges at the defects within their thermodynamic spaces, examining both local and global topology, and investigating how dilaton gravity parameters affect the thermodynamic topology of black holes compared to charged black holes in General Relativity. The paper derives the solution for topological charged black holes in dilaton gravity, discusses their thermodynamic properties, and explores the concept of thermodynamic topology. The thermodynamic topology is analyzed using the off-shell free energy method, which views black holes as topological defects. The study identifies the winding numbers associated with these defects, which classify black holes into different topological classes. The topological charge is calculated using Duan's φ-mapping technique, and the results show that the topological charge depends on the value of the topological constant (k) and the parameters of dilaton gravity. In the fixed charge ensemble, the topological charge is found to be zero for positive values of the cosmological constant (Λ) and either zero or one for negative values of Λ, depending on the value of α. In the fixed potential ensemble, the topological charge is found to be -1 for positive Λ and varies with the sign of Λ and other parameters. The study also highlights the differences in thermodynamic topology between charged black holes in dilaton gravity and those in General Relativity. The results show that the topological charge is influenced by the curvature of the hypersurface (k), the parameters of dilaton gravity, and the sign of the cosmological constant. The findings provide insights into the structural properties of black holes within the framework of thermodynamic topology.
Reach us at info@study.space
[slides and audio] Thermodynamic topology of topological charged dilatonic black holes