Calculus of Variations and Geometric Measure Theory
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Exotic solutions of the Einstein equations and gravitational shielding”

Alessandro Carlotto

created by paolini on 28 Sep 2016

4 oct 2016 -- 14:30   [open in google calendar]

Aula Dal Passo Dipartimento di Matematica Roma "Tor Vergata"


After a broad contextualisation, I will describe the recent construction (joint with Richard Schoen) of a new class of solutions to the Einstein constraint equations that exhibit highly anomalous properties both at a geometric and at a physical level. In the purely Riemannian setting our methods produce asymptotically flat manifolds that have positive ADM mass but are exactly flat outside a cone of arbitrarily small, pre-assigned opening angle. In particular, using basic facts about Huisken's isoperimetric mass one can see that these data contain arbitrarily large stable CMC spheres that are not isoperimetric for they volume they enclose. Furthermore, the gluing scheme that we develop allows to produce novel classes of N-body solutions for the Einstein equation, which patently exhibit the phenomenon of gravitational shielding: for any large T we can engineer solutions where any two massive bodies do not interact at all for any time up to T, in striking contrast with the Newtonian gravity scenario.

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