The Perturbation Of Cosmology And Black Holes In Horava-Lifshitz Gravity With Projectability Condition

General Relativity proposed by Einstein, which started a new era of gravity theory. With the general theory of relativity, people have a valid theoretical tool to investigate our solar system, galaxy, even whole universe. Nowadays, however, in the research of the gravity theory, there are still many important issues. For example, the conflict between general relativity and quantum mechanics (another branch of physics) in Planck scales, the unknown properties of the gravity in this scales and the way to quantize the gravity.Recently, Professor Petr Horava of California University put forward a new gravity theory, which in principle can avoid the difficulty that gravity theory can't renormalization. In this theory named as Horava-Lifshitz gravity, we can obtain general relativity in lower energy case, even though the Lorentz symmetry is breached because of higher order terms in the action, the difficulty about renormalization of gravity can be avoided. Horava-Lifshitz theory has been extensively interested by many theoretical physicists. At present, people have used this theory to research cosmology and black holes, and have obtained several significant results.This thesis studies the perturbation of cosmology and black holes in Horava-Lifshitz gravity with projectability condition. The research contents, innovation points and the main conclusions are as follows:1. We derived the field equations of Horava-Lifshtiz theory with projectability and detailed balance condition softly breaking. The equations are generalized of general relativity in high energy case, and they break the Lorentz symmetry at high energy case, but return to general relativity equations at low energy case. In our research, we introduced projectablity condition, which required that N=N(t) in metric with ADM form, namely N only depends on time. This condition can lead to few coupling constants of space curvature's scalars. With the projectablity condition, the action LV in Horava-Lifshitz theory just has ten terms, namely, cosmological constant term, R , R 2, , where the coupling constants of R term can be obtained by Einstein field equation, because this theory require that the gravity theory become general relativity at low energy case. Therefore, there are still undetermined coupling constants. We then introduce softly breached detailed balance condition to further reduce the number of coupling constants, and finally let the five coupling constants of higher terms ( RR_ij R_ij, R³, R_i^jR_l^j R_i^l, (?) become one coupling constant. This work makes the theory more beautiful.2. We introduce a scalar field with projectablility and detailed balance condition with softly breaking, and then study its instability, strong coupling and ghost in cosmological de Sitter spacetime. Our conclusion shows that, due to the projectability and detailed balance condition with softly breaking, the instability and ghost problem vanished, and strong coupling problem also could be resolved after consider the higher order terms in this theory.3. We study the quasinormal modes of black holes in Horava-Lifshitz gravity, and get the odd parity gravitational perturbation equation. We use this equation to research the eigenvalue of black holes'quasinormal frequency and stability of spacetimes. The results can be used for research the differences between black hole in Horava-Lifshitz theory and general relativity's black holes, and provide possible methods to test this theory.This research has solved several important difficulties of Horava-Lifshitz theory, and paves the way for study the quantization and renormalization of gravity by the theory in the future.We also introduced the vector into this theory, and obtained some charged Horava-Lifshitz exactly spacetime metric.In this thesis,μ,Ï…=0,1, 2, 3 and i, j =1, 2, 3This work is done in Institute for Theoretical Physics of Chongqing University, Department of Physics of Baylor University and Institute for Advanced Physics and Mathematics of Zhejiang University of Technology, and this research is supported in part by the National Natural Science Foundation of China.