Title: Gluing small black holes along timelike geodesics
Abstract: I will describe the construction of spacetimes modeling the merger of a very light black hole with a unit-mass black hole, followed by relaxation of the resulting single black hole to its equilibrium state. More generally, given a spacetime $(M,g)$ solving the Einstein field equations in vacuum and a timelike geodesic in $M$, I will explain how to construct a solution $g_\epsilon$ of the Einstein equations which is close to $g$ far from the geodesic but near any point along the geodesic approximately equal to the metric of a (Kerr) black hole with mass $\epsilon$. My first lecture will largely focus on the geometric aspects of the problem and the main results. (Scalar curvature will arise through the general relativistic constraint equations!) In my second lecture, I will discuss some of the analytic features of wave propagation on spacetimes that degenerate in this particular manner.
Antonio Auffinger
(847) 491-5524
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