Einstein’s theory describes gravity using the Levi-Civita connection, where curvature is the only non-trivial geometric field strength. More general geometric and gauge-theoretic frameworks allow the connection to carry torsion and nonmetricity as well, opening new possibilities for strong-field gravity.
In this talk I will focus on black holes and gravitational waves in theories beyond Riemannian geometry. I will first introduce the geometric framework behind Poincaré gauge gravity, metric-affine gravity, and teleparallel gravity, emphasizing how torsion and nonmetricity can be associated with new gravitational degrees of freedom. I will then discuss several strong-field applications. These include scalarized black holes in teleparallel scalar-Gauss-Bonnet gravity, exact black-hole solutions with torsion and nonmetricity carrying geometric hair, and slowly rotating black holes with axial torsion, where a gravitational spin-orbit effect appears. Finally, I will discuss gravitational-wave aspects of these theories, including the richer polarization structure of teleparallel Horndeski-type gravity and exact non-linear pp-wave solutions in metric-affine gravity. The goal is to show that modifying the geometry of spacetime is not only a formal extension of GR, but can lead to concrete signatures in black-hole physics and gravitational-wave propagation.
