Mathematical Methods for the General Relativistic Two-body Problem

Overview

LIGO’s discovery of gravitational waves in 2015 has led to a new era in astronomy. By the mid-2030s, we will be able to observe astrophysical gravitational-wave sources across multiple frequency bands, which will greatly advance our understanding of the physical Universe. Asymmetric binary systems will be a main source of gravitational waves, particularly in the multi-band era. The best way to model them is to expand Einstein’s field equations about the small mass ratio of the system. This use of perturbation theory in the relativistic two-body problem has been advanced in modern times by independent groups in different ways, which can make it difficult for the various approaches to be compared for consistency. Asymmetric binaries also bring about unique mathematical challenges in the statistical analysis of their gravitational-wave signals in detector data, as well as their broader characterisation in the active astrophysical environments where they typically form.

This week-long IMS workshop provides a chance for researchers from relevant communities to work together on solving the remaining challenges in the modelling and interpretation of gravitational waves from asymmetric binary systems. The workshop will be structured along three main themes: theory, computation, and science. Each theme will be addressed through a combination of invited talks and discussion sessions. The first of the invited talks in each theme will be a keynote talk that reviews the history and current status of research under that theme. Each subsequent talk will target a key challenge under each theme, and will be delivered by a leading expert on that specific topic. The discussion sessions will then expand upon the various topics covered by the invited talks, and will be chaired by relevant experts who will initiate and guide discourse among all the attendees of the workshop.