GEOMETRY OF FOUR-DIMENSIONAL UPPER HALF-PLANE AND ITS APPLICATION TO DOMAIN WALL SOLTION FOR N = 2 SUPERGRAVITY IN FIVE DIMENSION - Natanael Wijaya, Rio
We consider four-dimensional upper half-plane manifold and its application to N = 2 supergravity in five dimensions. This manifold is a generalization of Joyce metric, which is the main reference in this research. We start with the analysis of the stability condition for potential and Hamiltonian. The results of the analysis show that the stability of potential is closely related to Hamiltonian stability when the potential reaches its critical point. The analysis for the special case of upper half-plane metric in one parameter shows that the metric cannot be Einstein. Equation of motion from the Riemann-Hilbert action can be linearized to obtain the solution for the first order approximation. At the end of this dissertation, we talk about the application of Joyce metric to domain wall solution for N = 2 supergravity in five dimensions. We show that domain wall solution will reduce the four-dimensional problem to two-dimensional problem in upper half-plane. Stability condition from the flow equation is obtained from the Hessian matrix.