Regularization methods in general relativity
Divergent mathematical expressions arise in various problems in general relativity. In this talk I will present mathematical methods that can handle certain infinities that arise in problems of physical interest. First, I will consider a coalescing extreme mass ratio binary, where a compact object
(e.g. a solar mass black hole) inspirals towards a much more massive object (e.g. a supermassive black hole). The calculation of the gravitational radiation which is emitted from this binary can be simplified by using a perturbation analysis, where the smaller object is approximated by a point particle that produces metric perturbations on a fixed background spacetime, which is induced by the larger object. Future measurements with gravitational-wave detectors should be sensitive to information encoded in both the first-order and the second-order metric perturbations that are produced by this particle. Unfortunately, the standard expression for the second-order perturbations diverges. In this talk I will present a regularization method which is capable of providing a finite expression, to these otherwise ill-defined perturbations. Next, I will discuss genuine physical singularities that arise for example inside black holes, and present a mathematical model that can handle certain spacetime singularities at the classical level.