Symmetric teleparallel connection and spherical solutions in symmetric teleparallel gravity

In this article, we focus on symmetric teleparallel gravity, a modification of general relativity where gravity is described by the nonmetricity of an affine connection, whose curvature and torsion vanish. In these theories, the fundamental variables are the metric and an affine connection. Starting from the coincident gauge, a system of coordinates for which the affine connection coefficients vanish, we derive the most general connection for a spherically symmetric and stationary spacetime. We then derive the field equations in a specific class of symmetric teleparallel theories, the so-called newer general relativity. This theory is constructed from the five possible quadratic scalars of nonmetricity. We find two families of vacuum solutions that correspond to some exotic objects and we study their properties. In particular, we investigate the possibility of having a traversable wormhole, we compute the Komar mass, we discuss the conditions for asymptotic flatness, the existence of singularities, the radial motion and bound orbits of particles around these objects, the light deflection, as well as the causal structure of these spacetimes.