|Description||Doctor of Philosophy Oral Defense|
Advisor: Anzhong Wang
Two-Dimensional Horava-Lifshitz Theory of Gravity
Horava-Lifshitz gravity is one of the modified gravity theories which is power-counting renormalizable due to the anisotropic scaling between time and space. In this talk, I will mainly focus on the two-dimensional Horava-Lifshitz gravity. The classical solutions of both projectable and nonprojectable Horava gravity will be presented. When quantizing the theory in the canonical approach, the integral Hamiltonian constraint in the projectable case will generate the so-called Wheeler-DeWitt equation which can be exactly solved if the invariant length and its conjugate momentum are used as the new variables. On the other hand, for the nonprojectable case, the lapse function is no longer a Lagrangian multiplier but one of the canonical variables. This results in a local and second-class Hamiltonian constraint which can be solved for the lapse function. The quantization of nonprojectable case is carried out by directly dropping out the unphysical degrees of freedom. Then I will talk about how a non-relativistic scalar field can be added into the theory. In the projectable case, the minimal coupling is adopted and canonical quantization is implemented in the same way as in the pure gravity case. In the nonprojectable case, the non-minimal couplings will be employed and both Killing and Universal horizons are found from the classical solutions.