Bibhas Ranjan Majhi, Dibakar Roychowdhury
Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamical frame work, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature $2k$ in Horava-Lifshitz gravity at the Lifshitz point $z=3$. We find (a) for both $k=0$ and $k=1$, there is no phase transition, (b) while $k=-1$ case exhibits both second and first order phase transitions. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge whereas that for the first order phase transition is associated to the discontinuity of Hawking temperature. Near the critical point of the second order phase transition, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamical scaling laws.
View original:
http://arxiv.org/abs/1205.0146
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