GLOBAL EXISTENCE OF SOLUTIONS AND SPACE-TIME COMPLETENESS OF EINSTEIN-KLEIN-GORDON SYSTEM

• Main Author: Prisma Wijayanto, Mirda
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/79450
• Institution: Institut Teknologi Bandung

One of the open problems in general relativity is the study of gravitational waves which bring some information for many astronomical phenomena such as black holes collision, oscillation of the black hole horizon, etc. One attempt to study gravitational waves is to create a mathematical model where gravity is coupled with matter fields. One of the simple ways to do so is by introducing a minimally coupled term of a scalar (spin-0) field, also known as Klein-Gordon field, in the Einstein-Hilbert Lagrangian. The system formed is referred to as the Einstein-Klein-Gordon system. We study the existence of global classical solution to the Einstein-scalar equation in higher dimensions (D ? 4). In the starting point, we reduce the problem into a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using Banach fixed theorem, we show that there exists a unique fixed point, which is the solution of the main problem. For a given initial data, we prove the existence of a global classical solution. We also study the completeness properties of the space-time. Here, we introduce a mass-like function for D ? 4 in Bondi coordinates. The completeness of space-time along the future directed time-like lines outward to a region which resembles the event horizon of the black hole.