Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1088/1126-6708/2008/09/034
Keywords
differential and algebraic geometry; black holes
Categories
Funding
- Conacyt, Mexico [48601]
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We apply the formalism of geometrothermodynamics to the case of black holes with cosmological constant in four and higher dimensions. We use a thermodynamic metric which is invariant with respect to Legendre transformations and determines the geometry of the space of equilibrium states. For all known black holes in higher dimensions, we show that the curvature scalar of the thermodynamic metric in all the cases is proportional to the heat capacity. As a consequence, phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as true curvature singularities. We interpret this as a further indication that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.
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