Ehlers–Geren–Sachs theorem

The Ehlers–Geren–Sachs theorem is a result in general relativity that addresses the behavior of gravitational fields and the geometry of spacetime around certain kinds of distributions of matter. Specifically, it relates to the nature of gravitational waves and the properties of the spacetime in the presence of gravitational radiation. The theorem states that under suitable conditions, if a gravitational wave is present in a vacuum region of spacetime, then the geometry of the spacetime exhibits specific features.