Localizing solutions of the Einstein constraint equations

TL;DR

This paper develops a method to localize solutions of Einstein's constraint equations, enabling the construction of initial data with positive mass that are trivial outside small regions, and introduces novel N-body solutions demonstrating gravitational shielding.

Contribution

It introduces an optimal localization technique for Einstein constraint solutions and constructs new N-body solutions exhibiting gravitational shielding phenomena.

Findings

Constructed initial data with positive ADM mass localized outside small cones.

Developed a gluing scheme for Einstein constraint equations.

Produced N-body solutions with no gravitational interaction over finite times.

Abstract

We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class 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 $t\in(0,T)$, in striking contrast with the Newtonian gravity scenario.