On stationary solutions to the non-vacuum Einstein field equations

TL;DR

This paper establishes a local curvature estimate for stationary solutions to Einstein-Maxwell-Klein-Gordon equations, showing such solutions are flat under certain conditions, and extends the results to higher dimensions.

Contribution

It provides a new curvature estimate for stationary solutions and generalizes the flatness result to higher-dimensional spacetimes.

Findings

Stationary solutions with zero Poynting vector are flat.

The curvature estimate applies to four-dimensional solutions.

Results are extended to higher-dimensional cases.

Abstract

We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing Poynting vector and proper coupling constants (like dark energy) is flat. We also generalize the result to higher dimensions.