The Spacetime Thermodynamic Interpretation Of Ho(?)ava-Lifshitz Gravity

Among the four interactions in the universe, gravity is the first one that has been studied historically, and is also the last one that has not been quantized in the framework of local quantum field theory. It is generally expected that a thorough understanding of the black hole thermodynamics will help us to establish the quantum theory of gravity. It has extended the study of black hole thermodynamics to any spacetime with the horizon as the boundary of a thermodynamic system, viz. spacetime thermodynamics. Some generally properties about the gravity have been observed.As we all know, the general relativity is a non-renormalizable theory, lots of efforts has been made to construct renormolizable theories of gravity. Recently, a new theory of gravity was proposed by Horava, which is claimed to be a UV complete candidate for gen-eral relativity. It is natural to ask the question that does the so called Horava-Lifshitz theory also have the general properties which have been drawn from the spacetime thermodynam-ics.In this thesis, we interpret Horava-Lifshitz (H-L) gravity theory from the view point of spacetime thermodynamics.After a brief introduction of this problem and some relevant history, we review in Chapter 2 the chief results and perspective view of spacetime thermodynamics. The de-velopment and status of H-L gravity theory are reviewed in Chapter 3, including some discussions about the troubles of this theory and their way out.In Chapter 4, we first review the research of black hole phase transitions, and discuss how can the black holes in (deformed) H-L gravity also be treated as thermodynamic sys-tems. We study black hole phase transitions in H-L gravity, including the charged/uncharged topological black hole and KS black hole. We found very interesting phase structures in these black holes, some of the properties are not observed in Einstein gravity. Particularly, the stability properties of black holes in H-L gravity with small radius changed dramati- cally which can be considered as a leak of information about the small scale behavior of spacetime. The whole set of thermodynamical metrics for these black holes are also be constructed, their Ricci scalars are computed and analyzed. A new black hole local phase transition in H-L gravity that cannot be revealed by these thermodynamical metrics has been found.In Chapter 5, we illustrate that H-L gravity can indeed have a spacetime thermody-namic interpretation though two aspects of this theory.1) The field equation of (deformed) H-L gravity can be identified as the first law of thermodynamics at a spherically symmetric horizon.2) The Friedmann equation of (deformed) H-L theory can be cast to a form of the first law of thermodynamics at the apparent horizon of a FRW universe. In discussing the second point, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics associated with the apparent horizon in FRW universe is relative to the Kodama observers.In the concluding chapter, we summarize the progress that we have made and outline what deserves to be done in the next step.