Collection Number C21006
Collection Date -
Collection Type Conference/School
Numerical simulations of extereme mass ratio inspirals face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations of the self-force acting on point particles orbiting supermassive black holes. Such equations are distributionally sourced, and standard numerical methods, such as finite-difference or spectral methods, face difficulties associated with approximating discontinuous functions.
"In 2034 LISA is due to be launched, which will provide the opportunity to extract physics from stellar objects and systems that would not otherwise be possible, among which are EMRIs. Unlike previous sources detected at LIGO, these sources can be simulated using an accurate computation of the gravitational self-force, resulting from the gravitational effects of the compact object orbiting around the massive BH. Whereas the field has seen outstanding progress in the frequency domain, metric reconstruction and self-force calculations are still an open challenge in the time domain.
Our long-term goal is to calculate the Lorenz gauge gravitational self-force for an extreme mass-ratio binary system in Kerr spacetime. Past work in the time-domain has encountered time instabilities for the two lowest modes m=0 and m=1. In order to overcome this problem, we enter the frequency-domain, which introduces elliptic PDEs. To develop an appropriate scheme, we first investigate the scalar self-force in Kerr spacetime by separating the Φ and t variables. To calculate the self-force, we use the effective source method.
I will discuss the numerical methods we use to calculate the self-force on a scalar charge orbiting a Kerr black hole. We apply a 2nd-order finite difference scheme on a rectangular grid in the r*-θ plane. By working in the frequency domain and separating the ϕ variable (but not θ) we encounter elliptic PDEs, which present certain numerical challenges. One challenge is that every grid point is coupled to every other grid point so that a simultaneous solution requires solving a large linear system.
A multi-mode time-domain surrogate model for gravitational wave signals from comparable to extreme mass-ratio black hole binaries
We present EMRISur1dq1e6, a reduced-order multi-mode time-domain surrogate model of gravitational waveforms for non-spinning black hole binary systems with comparable- to extreme mass-ratio configurations. This surrogate model is trained on waveform data generated by a point-particle black hole perturbation theory (ppBHPT) framework computed from a high-performance Teukolsky equation solver code.
Analysing the data for the upcoming LISA mission will require extreme mass ratio inpsiral (EMRI) waveforms waveforms that are not only accurate but also fast to compute and extensive in the parameter space. To this end, we present a method for rapidly calculating the inspiral trajectory of EMRIs with a spinning primary.
Semi-analytic solutions are useful because they are much faster than full numerical evolutions by virtue of the fact that they do not have to use as many points to achieve similar levels of accuracy. Currently there exists a semi-analytic solution for spin precessing binaries, which is implemented in LIGO and used to generate waveforms for comparison with gravitational waves. This solution comes with a caveat: it was calculated using precession averaged equations and thus has an oscillating error associated with the unaccounted for precession.
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".