Conference

The scattering angle function exhibits a simple dependence on the mass ratio, which has been recently used to obtain new post-Newtonian (PN) results for arbitrary mass ratios from first-order self-force calculations. In this talk, I will present results for the spin-orbit coupling at fourth subleading PN order (5.5PN), including both local and nonlocal contributions, and the spin-squared coupling at third subleading PN order (5PN) for aligned spins. The spin-orbit results are missing one coefficient at second order in the mass ratio, and the spin-squared results are missing one coefficient at first order in the mass ratio. The latter could be determined from a self-force calculation of the spin-precession invariant for circular orbits in Schwarzschild to linear order in the spin of the small object. I will also discuss implications regarding the first law of binary mechanics with spin quadrupole and its relation to tidal invariants.

We will discuss an adiabatic waveform model for generic (eccentric, inclined) EMRI orbits in Kerr spacetime, based on a high-order PN expansion as well as an expansion in eccentricity to the (frequency-domain) Teukolsky equations.

To a first approximation, objects in general relativity move along geodesics. Looked at more closely, a body's internal structure can affect its motion. This talk will explore some of the surprising possibilities which arise when such effects are taken into account. An object can, for example, control its orbit merely by manipulating its internal structure: unstable orbits can be stabilized, bound orbits can be made unbound, and more, all without a rocket.

Since the advent of (relativistic) astrophysics it has been one of the most important tasks to study the motion of freely falling particles, both from a purely academic and an observational point of view. In this presentation I review the solution methods for the equations of motion of particle-like objects and light within a wide variety of spacetimes. Moreover, we take a closer look on the importance of special orbits for phenomena like black hole shadows or accretion discs.

"""Gravitational wave detectors and their increasing precision have enabled more specific tests of general relativity, including spectroscopic tests of black holes by measuring the quasinormal modes within the ringdown signal. These tests ideally compare the QNM frequencies to predictions from theories beyond GR, where black holes may be described by deformations to the Kerr metric. I will present a framework to compute the first order QNM shifts of these deformed Kerr Black Holes at arbitrary spin and present some initial results for the spin-0 case. In addition, I will lay out some of the technical issues that come up when computing the shifts for the spin-2 modes, and explain how they are surmountable."""

We study the stability of quasi-normal modes (QNM) in asymptotically flat black hole spacetimes by means of a pseudospectrum analysis. The construction of the Schwarzschild QNM pseudospectrum reveals: i) the stability of the slowest decaying QNM under perturbations respecting the asymptotic structure, reassessing the instability of the fundamental QNM discussed by Nollert (1996); ii) the instability of all overtones under small scale perturbations of sufficiently high frequency, that migrate to a universal class of QNM branches along pseudospectra boundaries, shedding light on Nollert & Price's analysis (1996).

In this talk we discuss current efforts to calculate the gravitational Green function and use it to calculate the self-force in Schwarzschild spacetime. We first calculate the Green function for the Regge-Wheeler equation. Then, using the Chandrasekhar transformation we are able to calculate the Green function for the spin-2 (radial) Teukolsky equation. By following the Chrzanowsky metric reconstruction procedure, we intent to obtain the Green function associated with the metric perturbation equation and, subsequently, the self-force.

We present an update on Green function methods for modelling Extreme Mass Ratio Inspirals. In particular, we present an accurate, efficient and robust procedure for computing the Green functions of the Regge-Wheeler and Zerilli equations, and show the application to the computation of self-force and energy flux results, considering a range of sample orbits from circular geodesics to unbound encounters. In addition, we demonstrate further possible applications and improvements to the method, including progress in extending it beyond the Regge-Wheeler-Zerilli formalism.

We describe the transition to plunge of a point particle around the last stable orbit of Kerr at leading order in the transition-timescale expansion. Taking systematically into account all self-force effects, we prove that the transition motion is still described by the Painlevé transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasi-circular adiabatic inspiral with the transition motion. The matching requires to take into account the secular change of angular velocity due to radiation-reaction during the adiabatic inspiral, which consistently leads to a leading-order radial self-force in the slow timescale expansion.

The motion of a radiating point particle in the Kerr spacetime can be represented by a series of geodesics whose constants of motion change slowly over its motion. In the case of energy and axial angular momentum, there are conserved currents, defined for the field, whose fluxes at infinity and the horizon directly determine the evolution of these constants of motion. This relationship between the properties of point-particle motion and fluxes of conserved currents is known as a "flux-balance law". Despite the flux-balance laws for energy and axial angular momentum, the third constant of motion in Kerr, the Carter constant, has no known flux-balance law. While there are conserved currents that can be defined for the field that are, in certain senses, "associated with the Carter constant", the fluxes of these currents are not clearly related to the Carter constant for the particle. In this talk, we present our recent efforts to find such flux-balance laws, in the case of a point particle in Kerr that is coupled to a scalar field.