Local existence of classical solution to the higher dimensional Einstein-Maxwell-Klein-Gordon system Mirda Prisma Wijayanto (a), Fiki Taufik Akbar (b), and Bobby Eka Gunara (b*)
a) Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman
Jl. Dr. Soeparno no. 61 Purwokerto, Indonesia, 53122
b) Theoretical High Energy Physics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Jl. Ganesha no. 10 Bandung, Indonesia, 40132
*bobby[at]itb.ac.id
Abstract
In this paper we study the existence of local classical solution to the coupled Einstein and Maxwell-Klein-Gordon system in higher dimensions. This system provides a toy model to study the dynamics of the complex scalar fields under the influence of the interaction of the gravitational and electromagnetic fields. In the starting point, we introduce the metric of the spacetime in the Bondi coordinate. Then, we construct the evolution equation in the form of a single first-order nonlinear integro-differential equation. Furthermore, we show that there exists a unique fixed point that is the solution of the main problem based on the contraction mapping arguments. Finally, for a given initial data, we prove the existence of a local classical solution.
Keywords: Higher dimensional gravity, Einstein equations, Maxwell-Klein-Gordon equations, local existence
