Regularization of self-fields in the gravitational two-body problem

In General relativity, sufficiently small bodies are idealized as test particles moving along spacetime geodesics. This picture becomes inadequate, however, once the object’s own gravitational field is taken into account. The self-force program resolves this by showing that compact objects still follow geodesic motion – not of the external spacetime, but of an effective metric that includes the influence of the object’s self field. The central technical challenge is that the self-field is singular at the worldline and must be carefully regularized so that only its regular piece contributes to the effective spacetime curvature. This construction is now well understood through first order in the mass ratio and has only been recently extended to second order.

In this talk, I present a general framework that implements this principle nonperturbatively, applicable to any covariant theory of gravity. Self-interaction effects are absorbed into systematic renormalizations of the object’s stress energy tensor, yielding equations of motion in which even strongly self-gravitating bodies move as test objects in a regular effective metric. I conclude by showing how this formalism can be applied to study tidal effects on strongly self-interacting bodies as well as to the Hamiltonian description of the conservative piece of their dynamics.