Gluing small black holes along timelike geodesics

Abstract: Suppose we are given a globally hyperbolic spacetime $(M,g)$ solving the Einstein vacuum equations, and a timelike geodesic in M. I will explain how to construct, on any compact subset of M, a solution geps of the Einstein vacuum equations which is approximately equal to g far from the geodesic but near any point along the geodesic approximately equal to the metric of a Kerr black hole with masseps. As an application, we can construct spacetimes which describe the merger of a very light black hole with a unit mass black hole, followed by the relaxation of the resulting single black hole to its equilibrium (Kerr or Kerr-de Sitter) state.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.