Abstract
Thermodynamics of $z=4$ Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz black holes in $3+1$ dimensions is studied in extended phase space. By using the scaling argument we find the Smarr relation and the first law for the black hole solutions of $z=4$ Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity. We find that it is necessary to take into account the variation of dimensionful parameters of the theory in the first law. We find that the reverse isoperimetric inequality can be violated for spherical, flat, and hyperbolic horizons and in all such cases we have black holes for which the specific heat at constant pressure and volume are positive. This provides a counterexample to a recent conjecture stating that black holes violating the reverse isoperimetric inequality are thermodynamically unstable. We find for $z=4$ Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz black holes with hyperbolic horizons that there are two critical points: one showing Van der Waals behavior, the other reverse Van der Waals behavior.
Highlights
The laws of black hole mechanics [1] have had a profound impact on our understanding of black hole physics
Of particular interest is the thermodynamics of black holes in asymptotically AdS spacetime, in which a negative cosmological constant is present
For k 1⁄4 −1 hyperbolic horizons, we see from the bottom panel of Fig. 6 that the reverse isoperimetric inequality is violated in two physical regions: small black holes and intermediate size black holes
Summary
The laws of black hole mechanics [1] have had a profound impact on our understanding of black hole physics. In this paper we study the thermodynamics of superrenormalizable Horava-Lifshitz black holes. Our study of z 1⁄4 4 Horava-Lifshitz gravity shows that in the superrenormalizable theory, there are two critical points of black hole thermodynamics. This is unlike the z 1⁄4 3 case where no criticality exists [48]. Using (34)–(37), along with the entropy (24) and the temperature (23), we find that the Smarr relation (27) for z 1⁄4 4 Horava-Lifshitz black holes is satisfied. We see that for the hyperbolic horizon, k 1⁄4 −1, the temperature possesses a single minimum in the small black hole branch to the left of the divergent point.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
