In the last quarter century, Capra has grown from a mere
handful of people to a fully international meeting, which now represents a
large diversity of interests. In that time, much progress has been made:
many aspects of the first order problem are now in hand, and a multitude
of techniques has been formulated for eventually use in full EMRI waveform
generation. Yet, much needs to be done, most notably at second order. In
Capra meetings of the past, we have often recognized the need to reach out
to the younger generation. I think efforts in that direction have clearly
been effective. At some Capra meetings, specific problems have often
taken focus, both in discussions at the meeting, and in the work that
evolves over the coming year. From experience, we know this approach has
also clearly paid off. From the discussions that have taken place here,
we need to go forward with specific goals for the year ahead, drawing
wherever possible on the diversity we now have before us. Great things
can be achieved if great problems are tackled. What have we formulated to
work on as a community together before we can meet again in 2022?
The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ~ 0.1, the nonvanishing quadrupolar Love tensors are ~ 0.002, thus showing that black holes are particularly "rigid" compact objects. We also show that the induced quadrupole moments are closely related to the physical phenomenon of tidal torquing of a spinning body interacting with a tidal gravitational environment.
