Speaker
Description
General Relativity (GR) has been consolidated as the most successful theory to describe gravitation, having been confirmed by numerous experiments, most notably the direct detection of gravitational waves. However, GR presents limitations in different regimes: on cosmological scales, dark matter and dark energy are invoked to explain observational phenomena; on microscopic scales, the absence of a consistent quantum formulation motivates theoretical extensions. In this context, alternative theories of gravitation have been proposed, among which those based on metric-affine geometries stand out, where curvature, torsion, and non-metricity can be treated as independent fields.
Among these approaches, Symmetric Teleparallel Gravitation (STG) attribute gravitational effects exclusively to non-metricity, imposing vanishing curvature and torsion. A particular case, the Symmetric Teleparallel Equivalent of General Relativity (STEGR), is shown to be equivalent to GR. In this work, a more general formulation of STG is investigated, defined by a linear combination of the possible self-contractions of the non-metricity tensor, with free coefficients that characterize different theoretical sectors.
The analysis was carried out in the weak-field regime, employing the Palatini formulation and the coincident gauge, which simplifies the equations by allowing non-metricity to be expressed as derivatives of the metric. Two main scenarios were considered: (i) the Newtonian limit, in which constraints among the coefficients are required to recover consistency with classical gravitation; and (ii) wave solutions, in which the propagation of gravitational perturbations was studied. It was shown that different combinations of coefficients lead to distinct numbers of degrees of freedom and gravitational wave polarization modes. In particular, beyond the usual tensorial polarizations (+ and ×), additional modes arise, such as the scalar breathing mode and longitudinal modes, absent in GR.
Thus, the results reveal a new phenomenology of gravitational waves, opening the possibility of observational signatures capable of distinguishing GR from alternative theories based on non-metricity. The classification of theoretical sectors obtained provides clear criteria for consistency with classical limits and for predicting new oscillation modes, contributing to the advancement of the understanding of the geometric foundations of gravitation.
