Geometrothermodynamics of five dimensional black holes in Einstein-Gauss-Bonnet-theory

Abstract

We investigate the thermodynamic properties of 5D static and spherically symmetric black holes in (i) Einstein-Maxwell-Gauss-Bonnet theory, (ii) Einstein-Maxwell-Gauss-Bonnet theory with negative cosmological constant, and in (iii) Einstein-Yang-Mills-Gauss-Bonnet theory. To formulate the thermodynamics of these black holes we use the Bekenstein-Hawking entropy relation and, alternatively, a modified entropy formula which follows from the first law of thermodynamics of black holes. The results of both approaches are not equivalent. Using the formalism of geometrothermodynamics, we introduce in the manifold of equilibrium states a Legendre invariant metric for each black hole and for each thermodynamic approach, and show that the thermodynamic curvature diverges at those points where the temperature vanishes and the heat capacity diverges.

New sections added, references added

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• A consistent and unified picture for critical phenomena of $f(R)$ AdS black holes
• Understanding Gravitational Entropy of Black Holes: A New Proposal via Curvature Invariants
• On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
• A geometric approach to the thermodynamics of the van der Waals system
• Quantum Tunneling of Spin-1 Particles from a 5D Einstein-Yang-Mills-Gauss-Bonnet Black Hole Beyond Semiclassical Approximation
• Geometric description of the thermodynamics of a black hole with power Maxwell invariant source
• Area Functional Relation for 5D-Gauss-Bonnet-AdS Black Hole