Symmetries in the gravitational physics of black holes

The gravitational physics of black holes exhibits profound connections to symmetry
 principles across all phases of binary coalescence. We explore how symmetry arguments illuminate three key observables: tidal Love numbers, quasi-normal modes, and gravitational memory.
During the inspiral, tidal Love numbers describe the conservative response of compact objects to external tidal fields. We revisit their vanishing for black
 holes in General Relativity from a symmetry-based perspective, examining how this property is altered in beyond-GR theories or by external environments.
In the ringdown, quasi-normal modes encode the characteristic oscillations of perturbed black holes. We discuss isospectrality between different parity
 sectors and its connection to the underlying symmetry structure of spacetime.
Finally, gravitational memory describes the permanent imprint on freely falling detectors after a passing gravitational wave. We explore its connection to
 Bondi-Metzner-Sachs symmetries at future null infinity in synchronous coordinates and discuss the associated soft theorems for scattering amplitudes and in-in correlation functions.