Propagation of gravitational waves in symmetric teleparallel gravity theories

TL;DR

This paper studies gravitational wave propagation in symmetric teleparallel gravity, showing all waves travel at light speed and identifying conditions for different polarization modes within a broad class of theories.

Contribution

It analyzes wave speeds and polarizations in the general 'newer general relativity' class of symmetric teleparallel gravity theories, revealing multiple polarization possibilities.

Findings

All gravitational waves propagate at the speed of light.

The number of polarization modes depends on the theory's parameters.

Some theories allow only two polarization modes, like general relativity.

Abstract

Symmetric teleparallel gravity (STG) offers an interesting third geometric interpretation of gravitation besides its formulation in terms of a spacetime metric and Levi-Civita connection or its teleparallel formulation. It describes gravity through a connection which is not metric compatible, however is torsion and curvature free. We investigate the propagation velocity of the gravitational waves around Minkowski spacetime and their potential polarizations in a general class of STG theories, the so-called "newer general relativity" class. It is defined in terms of the most general Lagrangian that is quadratic in the nonmetricity tensor, does not contain its derivatives and is determined by five free parameters. In our work we employ the principal symbol method and the Newman-Penrose formalism, to find that all waves propagate with the speed of light, i.e., on the Minkowski spacetime light cone, and to classify the theories according to the number of polarizations of the waves depending on the choice of the parameters in the Lagrangian. In particular it turns out that there exist more theories than just the reformulation of general relativity which allow only for two polarization modes. We also present a visualization of the parameter space of the theory to better understand the structure of the model.