Abstract

The radiative dynamics in a gravitationally-bound two-body system with a small mass ratio can be described using a perturbative approach whereby corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in the mass ratio, invoking the notion of ``gravitational self-force’’. The ongoing experimental effort to detect gravitational waves has in the past two decades motivated a program to obtain a rigorous formulation of the self-force and apply it numerically to describe the gravitational-wave signature of relevant inspiralling compact objects. I will review the theory of gravitational self-force in curved spacetime, describe how this theory is being implemented today in actual calculations, and discuss current frontiers. I will show results from recent calculations of gauge-invariant post-geodesic effects (like the finite-mass corrections to the rates of periastron advance and spin precession), and highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.