Testing fundamental physics with gravitational waves

<!--HTML--><p>The landmark detection of gravitational waves (GWs) has opened a new era in physics, giving access to the hitherto unexplored strong-gravity regime, where spacetime curvature is extreme and the relevant speed is close to the speed of light. In parallel to its countless astrophysical applications, this discovery can have also important implications for fundamental physics. In this context, I will discuss some outstanding, cross-cutting problems that can be finally investigated in the GW era: the nature of black holes and of spacetime singularities, the limits of classical gravity, the existence of extra light fields, and the effects of dark matter near compact objects. Future GW measurements will provide unparalleled tests of quantum-gravity effects at the horizon scale, exotic compact objects, ultralight dark matter, and of general relativity in the strong-field regime.</p>