Abstracts

Salvatore Capozziello

Gravitational waves in nonmetric gravity

We investigate gravitational waves in theories of gravity described by a non-metric compatible connection, free from torsion and curvature, known as symmetric-teleparallel gravity. We show that these theories exhibit only two massless and tensor modes. Their polarizations are transverse with helicity equal to two, exactly reproducing the plus and cross tensor modes typical of General Relativity. In order to analyze these gravitational waves, we first obtain the deviation equation of two trajectories followed by nearby freely falling point-like particles and we find it to coincide with the geodesic deviation of General Relativity. This is because the energy-momentum tensor of matter and field equations are Levi-Civita covariantly conserved and, therefore, free structure-less particles follow, also in non-metric gravity, the General Relativity geodesics. Equivalently, it is possible to show that the curves are solutions of a force equation, where an extra force term of geometric origin, due to non-metricity, modifies the autoparallel curves with respect to the non-metric connection. In summary, gravitational waves produced in non-metric theories of gravity behave as those in torsion-based gravity and it is not possible to distinguish them from those of General Relativity only by wave polarization measurements. This shows that the situation is different with respect to the curvature-based theories of gravity where additional scalar modes emerge for extensions and are rigorously two only for the Einstein-Hilbert theory.