Abstract:
Constructing a quantum theory of gravity using conventional approaches is one of the most fascinating but complicated problems in theoretical physics. Nevertheless, recent developments in this subject using path integral formalism appear to give promising results, at least in the semiclassical regime. By doing an imaginary time continuation, one can arrive at a path integral representation of the partition function of the theory. This allows us to use the machinery of statistical mechanics to find thermodynamic quantities associated with the system. In the case of gravity, one can compute the leading contribution to entropy and its corrections due to quantum fluctuations around classical solutions. Here we will study black hole solutions in three and four-dimensional Einstein gravity and calculate the entropy of some of these spacetimes up to one-loop order. The thesis is divided into seven chapters. In chapter 1, we will motivate the problem, briefly discuss the known results and outlines our approach. All the basic concepts and notations are presented in chapter 2. In chapter 3, we will discuss the path integral formalism of gravity and motivate the Euclidean continuation. Blackhole solutions and their Euclidean counterparts will be discussed in detail in chapter 4. In chapter 5, we will formally define entropy from a path integral perspective and calculate the leading order contributions. We will explicitly calculate the one-loop correction to the entropy of BTZ-black holes in chapter 6 and match our answers with the known results.
Finally, in chapter 7, we will summarize our results and discuss a few possible ways in which the study can be extended.
