Non-Gaussianities in Black Hole Perturbation Theory

We will discuss recent progress in understanding non-linear Love numbers and gravitational wave tails in black hole perturbation theory. In the first part, I will present new findings demonstrating that GR black holes possess an infinite number of vanishing non-linear tidal Love numbers. These results are derived systematically through matching a worldline effective field theory with axisymmetrically deformed black holes in full GR, revealing deeper symmetry structures that constrain black hole tidal responses beyond the linear regime. In the second part, I will discuss the generation of gravitational-wave tails arising from non-linear perturbations during the ringdown phase. Remarkably, they decay more slowly than the well-known linear Price tails, indicating that at late times, non-linear effects dominate the gravitational-wave signal.