Rigid covariance as a natural extension of Painlev\'e--Gullstrand space-times: gravitational waves

TL;DR

This paper explores a natural extension of Painlevé-Gullstrand space-times using rigid motions, providing a new coordinate system for gravitational waves, specifically applied to linear plane wave solutions.

Contribution

It introduces a novel approach to coordinate systems in General Relativity based on rigid motions, extending Painlevé-Gullstrand space-times and applying it to gravitational wave models.

Findings

Developed a natural extension of Painlevé-Gullstrand space-times.

Constructed a rigid coordinate system for gravitational linear plane waves.

Demonstrated the application to the cross mode of gravitational waves.

Abstract

The group of rigid motions is considered to guide the search for a natural system of space-time coordinates in General Relativity. This search leads us to a natural extension of the space-times that support Painlev\'{e}--Gullstrand synchronization. As an interesting example, here we describe a system of rigid coordinates for the cross mode of gravitational linear plane waves.