We consider spin-orbit ("geodetic") precession for a compact binary in strong-field gravity. Specifically, we compute ψ, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body of mass m1 and spin s1, with s1 Gm 2 1 /c, orbiting a non-rotating black hole. We show that ψ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for ψ at next-to-next-toleading order, and a Lorenz-gauge gravitational self-force calculation for ψ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the Effective One-Body model of the gravitational two-body problem. We conclude that ψ complements the Detweiler redshift z as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.

We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These bound states decay with time, due to the absence of superradiance in the (single-particle) Dirac field. We introduce a practical method for computing the spectrum of energy levels and decay rates, and we compare our numerical results with known asymptotic results in the small-M µ and large-M µ regimes. By applying perturbation theory in a horizon-penetrating coordinate system, we compute the 'fine structure' of the energy spectrum, and show good agreement with numerical results. We obtain data for a hyperfine splitting due to black hole rotation. We evolve generic initial data in the time domain, and show how Dirac bound states appear as spectral lines in the power spectra. In the rapidly-rotating regime, we find that the decay of low-frequency co-rotating modes is suppressed in the (bosonic) superradiant regime.We conclude with a discussion of physical implications and avenues for further work. * s.dolan@sheffield.ac.uk † ddempsey1@sheffield.ac.uk

We study wave propagation in a draining bathtub: a fluid-mechanical black hole analogue in which perturbations are governed by a Klein-Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose that a `pulse' disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation numerically in the time domain using the method of lines. Starting with Gaussian initial data, we demonstrate that a pulse will propagate along a null congruence and thus trace out the light-cone of the effective geometry. Our numerical results reveal features, such as wavefront intersections, frame-dragging, winding and interference effects, that are closely associated with the presence of null circular orbits and the ergosphere.Comment: 12 pages, 2 figures. Proceedings for III Amazonian Symposium on Physic