Abstract:
The tidal response problem for black holes is a fascinating problem on its own for various reasons. I will focus on the theoretically more interesting aspect of the naturalness concerns raised from some seemingly fine-tuned properties of the tidal deformability parameters (Love numbers) for general-relativistic black holes. This hints at the existence of an enhanced symmetry structure in the appropriately defined domain. We have indeed identified such an enhanced (Love) symmetry that precisely captures all the otherwise unnatural properties of static Love numbers. In this talk, I will review how the tidal response problem is formulated in a diffeomorphism invariant theory of gravity, such as GR, within the framework of the worldline EFT and how the black hole Love numbers are matched onto the microscopic computations from solving the Teukolsky equation. I will then show how the globally defined SL(2,R) Love symmetry arises and revives the theory’s naturalness at the classical level. Last, some remarkable generalizations of the Love symmetry will be presented, such as its extension to an infinite-dimensional algebra, a subalgebra of which reduces to the well-known enhanced isometry group of the near-horizon geometry of extremal black holes.