Asymptotic Lifshitz-like Solution In Lovelock Gravity (n=3)

As well known, Einstein's theory of general relativity has achieved great success. Along with the progresses of the experimental observations, especially the cosmic microwave background radiation, dark matter and dark energy, the original cosmological model need to be developed. There are various corrections to original Einstein gravitational field equation proposed in many papers in past years, one of which was Lovelock correction. In present essay, I will discuss some topics in Lovelock gravity.The main goal of this essay is to study the Lifshitz-like solution in Lovelock gravity. Horava inspirited from the Lifshitz solid theory of inspiration, got a regularized theory of gravity. After introducing the second and third terms of Lovelock action into the original of Einstein gravity equation, by the variation method, one can obtain the equations of motion for gravity field, and then get the classical Lifshitz solution. We get not only the pure gravitational solution, but also the solution contain the electromagnetic field and gravitational field. Besides, we also analyze the black hole solution and the thermodynamic properties of black brane solution.The present paper is organized as following. In Chapter 1 and Chapter 2, I review some necessary fundament about black hole and Horava-Lifshitz gravity. Then, I will discuss how to find Lifshitz-like solutions in Lovelock gravity and related thermodynamic quantities such as viscosity. Some discussions about the results are given in Ch.4. We also list a few questions to be considered in future...