Hawking Radiation, Black Hole Phase Transition And First Law Of Thermodynamics In H(?)rava-Lifshitz Theory

The foundation of black hole thermodynamics reveal the close relationship between quantum theory, statistical physics and thermodynamics. Therefore, it has important theoretical significances to study some basic properties for black hole thermodynamics. This thesis is devoted to the investigation of some basic problems concerned by black hole physicist, including Hawking radiation, black hole phase transition and the first law of thermodynamics in the Horava-Lifshitz theory. Some works have been done as follows:First, the Hawking temperature of the general static spherically symmetric black hole was investigated in the framework of Hamilton-Jacobi model proposed by the Indian scholar Rabin Banerjee et al. Making use of the dimension reduc-tion technique, considering the complete form for the action of emitted particle and according to the energy of emitted particle in the semiclassical situation, they obtained the conclusion that the Hawking temperature was corrected. Due to the relationship between the Hawking temperature and the energy of tunneling par-ticle, i.e.Γ∝e-2ImI= e(?), we know that the suitable energy definition of tunneling particle is important to obtain the correct Hawking temperature. We think that the emitted particle's energy should be changed accordingly when the complete form for the action of emitted particle was considered. The Hawking temperature for various energy definition were investigated in this paper and we found that the temperature is invariant if we adopt the standard energy definition (?) To further support our conclusion, the entropy for various energy de-finition was also calculated in this paper and we found that the semiclassical black hole entropy is always Bekenstein-Hawking entropy, i.e. S=A/4, whatever the definition of energy was adopted. Then making use of the first law of thermody-namics, we conclude that the Hawking temperature is invariant. The consistency of these two results also proves the correctness of our conclusion.Second, a new gravitational theory so called Horava-Lifshitz theory was pro-posed by Horava in the end of 2008 and the new theory has been investigate extensively since it was proposed. We focused on the KS black hole which is asymptotically flat and investigated phase transition and the first law of thermo-dynamics. Some main results contain:(1) different phase transition point was got by using equilibrium fluctuation method and non-equilibrium fluctuation method before, but the consistent phase transition point was obtained for KS black hole in this paper by using these two different methods; (2) although there is only one parameter mass for KS black hole, the second order phase transition also exists for it and the phase transition point is located at (3) assuming the Benkenstain-Hawking entropy hold for KS black hole and viewing the theoretical parameterωas a new state parameter, we obtained the new expression of the first law of thermodynamics for KS black hole. Then, we proved the previous assumption, i.e. Bekenstein-Hawking entropy also hold for KS black hole.