Existence of Local Classical Solution to the Einstein-Scalar System in Higher Dimensions Mirda Prisma Wijayanto, Fiki Taufik Akbar, Bobby Eka Gunara
Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no. 10 Bandung, Indonesia, 40132
Abstract
In this paper we study the existence of local classical solution to the Einstein-scalar equation in higher dimensions. 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 the unique fixed point, which is the solution of the main problem. Finally, for a given initial data, we prove the existence of a local classical solution.
Keywords: Einstein-scalar equation, higher dimensions, local existence
