Geometrothermodynamics in Hořava–Lifshitz gravity

Abstract

We investigate the thermodynamic geometries of the most general static,\nspherically symmetric, topological black holes of the Ho\\v{r}ava--Lifshitz\ngravity. In particular, we show that a Legendre invariant metric derived in the\ncontext of geometrothermodynamics for the equilibrium manifold reproduces\ncorrectly the phase transition structure of these black holes. Moreover, the\nlimiting cases in which the mass, the entropy or the Hawking temperature vanish\nare also accompanied by curvature singularities which indicate the limit of\napplicability of the thermodynamics and the geometrothermodynamics of black\nholes. The Einstein limit and the case of a black hole with flat horizon are\nalso investigated.\n