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Inspiral, transition and plunge: a framework for complete waveforms in the small-mass-ratio expansion

par Kuchler, Lorenzo
Président du jury Maris, Ioana Codrina
Promoteur Compère, Geoffrey ;Hertog, Thomas
Publication Non publié, 2023-09-04

Thèse de doctorat

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Résumé :

Gravitational waves are ripples in spacetime predicted by Einstein's theory of general relativity. Their first direct observational evidence came with the detection of a gravitational wave signal by the two LIGO interferometers in 2015, marking a historic event in gravitational physics. Accurate theoretical waveform templates are needed to detect the signals and to extract the information carried by gravitational waves. The space-based LISA interferometer, expected to fly in the mid-2030s, will be able to observe gravitational waves from sources that lie outside the sensitivity band of ground-based detectors. An example are extreme-mass-ratio inspirals (EMRIs), binary systems composed of a stellar-mass compact object (the "secondary") and a supermassive black hole (the "primary"). EMRIs can be modelled using gravitational self-force theory: the small body is treated as a perturbation to the background spacetime of the primary. The motion is driven by a self-force, which arises from the interaction of the secondary with its own gravitational field. Although originally designed to describe EMRIs, the self-force formalism was found to be applicable also for binaries with intermediate mass ratios and nearly comparable masses. A few such systems have already been observed by the ground-based detectors of the LIGO-Virgo-KAGRA Collaboration, and current modelling techniques struggle to accurately describe them. In this thesis, motivated by the prospect of detecting gravitational waves from binaries with small mass ratios, we study the motion of a non-spinning secondary in the spacetime of a supermassive primary. We restrict our analysis to quasi-circular orbits lying in the equatorial plane. The dissipative effect of the self-force leads to the secular decay of the orbit and to the final merger of the binary. The orbital motion can be divided into three stages. As long as the two bodies are at large orbital separations, the quasi-circular inspiral is characterized by two disparate timescales: the orbital period, on which the trajectory is approximately geodesic, and the radiation-reaction timescale, inversely proportional to the small mass ratio, on which the orbital parameters evolve. In the approach of the innermost stable circular orbit (ISCO), the motion loses its quasi-circular and slowly-evolving fashion, and the two-timescale approximation used to describe the inspiral breaks down. The motion on the ISCO-crossing timescale is known as the transition to plunge. Finally, the small body plunges behind the event horizon of the primary on a nearly geodesic orbit. In the first part of this thesis we present the scientific potential that lies in the detection of systems with small mass ratios and discuss the shortcomings of current modelling techniques. We give an overview of self-force theory and its description of the quasi-circular inspiral, in remarkable agreement with numerical relativity simulations for the coalescence of compact objects with nearly comparable masses. We then turn to the original results of this thesis: the first part deals with the orbital motion of a small body in Kerr spacetime. We derive an approximation scheme that describes the transition to plunge within self-force theory and asymptotically match it with the quasi-circular inspiral in the region where they overlap, laying the foundations for waveform templates that extend beyond the ISCO. In the second part we consider a Schwarzschild background. We complete the description of the equatorial motion by including the final plunge and asymptotically matching it to the transition regime. Furthermore, we treat the orbital motion in conjunction with the expanded Einstein field equations and derive explicit expressions for the self-force. The asymptotic matching procedure allows us to write composite solutions that seamlessly interpolate between the three regions. We build a framework that allows us to compute complete waveform templates within self-force theory that extend beyond the ISCO and are sufficiently accurate for detection and parameter estimation purposes. We compute leading-order adiabatic waveforms, obtaining a promising agreement with numerical relativity simulations in the regime of nearly comparable masses.