The 24th Capra meeting on Radiation Reaction in General Relativity

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 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).

"""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."""

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.

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.

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.

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 present a method to extract the redshift factor in numerical relativity simulations by means of its connection to the surface gravity. We proceed to analyze the small mass ratio limit and extract 2nd and higher orders in the case of non-spinning, quasi-circular binaries. We also compare our results to analytic post-newtonian and self-force calculations.

In this work we compare two approaches to modeling binary black holes (BBHs): 1) small mass-ratio (SMR) perturbation theory, and 2) numerical relativity (NR). We extend recent work on combining information from quasicircular nonspinning NR simulations of BBHs with results from SMR perturbation theory to nonspinning eccentric BBHs. We produce a dataset of long and accurate eccentric nonspinning NR simulations with the Spectral Einstein Code (SpEC) from mass ratios 1 to 10, and eccentricities up to 0.7. We analyze these NR simulations, compute gauge invariant quantities from the gravitational radiation, and develop tools to map points in parameter space between eccentric NR and SMR waveforms. Finally, we discuss discrepancies between SMR and NR predictions for the energy and angular momentum fluxes due to eccentricity, and limitations of such comparisons due to the limited parameter space in mass ratio covered by the NR simulations.

"We propose and explore a method for alleviating the scale disparity in numerical relativity simulations with mass ratios in the intermediate astrophysical range ($10^2 \lesssim q\lesssim 10^4$), where purely perturbative methods may not be adequate. A region around the smaller object considerably smaller than its horizon is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. We develop the basic idea and try it on the toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the scalar field as a linear perturbation in a 1+1D framework. Collaborators: Mekhi Dhesi, Adam Pound, Leor Brack, Harald Pfeiffer"