Contact geometry and thermodynamics of black holes in AdS spacetimes

Abstract

In this paper we discuss a formulation of extended phase space thermodynamics of black holes in Anti de Sitter (AdS) spacetimes from the contact geometry point of view. Thermodynamics of black holes can be understood within the framework of contact geometry as flows of vector fields generated by Hamiltonian functions on equilibrium submanifolds in the extended phase space that naturally incorporates the structure of a contact manifold. Deformations induced by the contact vector fields are used to construct various maps among thermodynamic quantities. Thermodynamic variables and equations of state of Schwarzschild black holes are mapped to that of Reissner-Nordström black holes in AdS, with charge as the deformation parameter. In addition, the equations of state of general black holes in AdS are shown to emerge from the high-temperature ideal gas limit equations via suitable deformations induced by contact vector fields. The Hamilton-Jacobi formalism analogous to mechanics is set up, and the corresponding characteristic curves of contact vector fields are explicitly obtained to model thermodynamic processes of black holes. Extension to thermodynamic cycles in this framework is also discussed.

32 pages, 1 figure

References in corpus (10)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Geometrothermodynamics
• Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
• Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
• A Hamilton-Jacobi Formalism for Thermodynamics
• Quantization of Contact Manifolds and Thermodynamics
• The first laws of thermodynamics of the (2+1)-dimensional BTZ black holes and Kerr-de Sitter spacetimes
• Stringy Generalization of the First Law of Thermodynamics for Rotating BTZ Black Hole with a Cosmological Constant as State Parameter
• Para-Sasakian geometry in thermodynamic fluctuation theory
• A geometric approach to solve time dependent and dissipative Hamiltonian systems

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