In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.
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.
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.
The prospect of gravitational wave astronomy with EMRIs has motivated increasingly accurate perturbative studies of binary black hole dynamics. Studying the apparent and event horizon of a perturbed Schwarzschild black hole, we find that the two horizons are identical at linear order regardless of the source of perturbation. This implies that the seemingly teleological behaviour of the linearly perturbed event horizon, previously observed in the literature, cannot be truly teleological in origin.
We show that perturbations of massless fields in the Kerr black hole background enjoy a hidden infinite-dimensional ("Love") symmetry in the properly defined near zone approximation. Love symmetry mixes IR and UV modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses (Love numbers) of static and spinning black holes. Generators of the Love symmetry are globally well defined and have a smooth Schwarzschild limit. The Love symmetry contains an SL(2,R)×U(1) subalgebra.
Black holes are never isolated in realistic astrophysical environments; instead, they are often perturbed by complicated external tidal fields. How does a black hole respond to these tidal perturbations? In this talk, I will discuss both the conservative and dissipative responses of the Kerr black hole to a weak and adiabatic gravitational field. The former describes how the black hole would change its shape due to these tidal interactions, and is quantified by the so-called “Love numbers”.
"One of the primary sources for the future space-based gravitational wave detector, the Laser Interferometer Space Antenna, are the inspirals of small compact objects into massive black holes in the centres of galaxies. The gravitational waveforms from such Extreme Mass Ratio Inspiral (EMRI) systems will provide measurements of their parameters with unprecedented precision, but only if the waveforms are accurately modeled. Here we explore the impact of transient orbital resonances which occur when the ratio of radial and polar frequencies is a rational number.
In recent work, tidal resonances induced by the tidal field of nearby stars or black holes have been identified as potentially significant in the context of extreme mass-ratio inspirals (EMRIs). These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a ‘jump’ leading to a shift in the phase of the gravitational waveform. We study how common and important such resonances are over the entire orbital parameter space.