Global existence of the solution to Einstein-Maxwell equations with small initial data

TL;DR

This paper proves that small initial data for the Einstein-Maxwell equations on four-dimensional space lead to solutions that exist for all time, using wave and Lorentzian gauge techniques.

Contribution

It establishes the global existence of solutions to the Einstein-Maxwell system under small initial data conditions, employing novel gauge-based estimates.

Findings

Global solutions exist for small initial data

Method relies on wave and Lorentzian gauge conditions

Provides estimates ensuring long-term existence

Abstract

We study the global existence of Einstein-Maxwell(EM) equations on $\mathbb{R}^4$. We use the method, which relies on wave and Lorentzian gauge conditions, to obtain some exquisite estimates. Our main conclusion is that if the initial data is small enough, then the EM system has a global in time solution.