Tidal forces are gravitational waves

TL;DR

This paper demonstrates that tidal forces in general relativity are a manifestation of gravitational waves, providing a new perspective and test for the propagation speed of gravitational effects.

Contribution

It reveals that tidal forces are a hidden form of gravitational waves, linking local effects to wave propagation and offering a new test for the speed of gravitational effects.

Findings

Tidal forces are caused by gravitational waves in general relativity.

Magnetic part of the Weyl tensor mediates tidal forces.

Proposes a new test for the speed of gravitational effects.

Abstract

In this paper we show in a covariant and gauge invariant way that in general relativity, tidal forces are actually a hidden form of gravitational waves. This must be so because gravitational effects cannot occur faster than the speed of light. Any two body gravitating system, where the bodies are orbiting around each other, may generate negligible gravitational waves, but it is via these waves that non-negligible tidal forces (causing shape distortions) act on these bodies. Although the tidal forces are caused by the electric part of the Weyl tensor, we transparently show that some small time varying magnetic part of the Weyl tensor with non zero curl must be present in the system that mediates the tidal forces via gravitational wave type effects. The outcome is a new test of whether gravitational effects propagate at the speed of light.