On the one hand, black holes are at the centre of the recent experiments to probe the strong-gravity frontier. On the other hand, at the centre of black holes, General Relativity develops inconsistencies. This exciting dichotomy points to new physics at some, as of now untested, intermediate curvature scale. Motivated by the principles of effective field theory, I will present three routes to constrain said new physics to recent and future observations.
1) Shadows: The image of a black hole taken by a distant observer directly probes the underlying stationary and axisymmetric background spacetime. Without having to specify any particular dynamics, I will discuss general parameterizations and their connection to fundamental-physics principles like (i) regularity (no remaining curvature singularity), (ii) simplicity (a single new-physics scale), and (iii) locality (a new-physics scale set by local curvature).
2) Stability: Specifying the linearized dynamics around black-hole spacetimes determines the onset of potential instabilities and connects to the ringdown phase of gravitational waves. I will discuss how the resulting instability constrains new physics in regimes of relevance for low-scale theories of dark energy and ultralight dark-matter scenarios.
3) Non-linear evolution: The stronger the probed curvature scale, the stronger the constraints on new physics. Hence, the non-linear regime of binary mergers is a particularly precious target. This requires the full numerical evolution of specific well-motivated and well-posed non-linear dynamics beyond General Relativity. I will present recent progress towards achieving such evolution for the effective field theory of gravity up to quadratic order in curvature.