A Gluing Construction Regarding Point Particles in General Relativity

TL;DR

This paper introduces a new gluing method for Einstein constraint solutions, enabling the construction of initial data with point-particle limits, extending previous models like Schwarzschild-de Sitter.

Contribution

It develops a novel gluing construction that combines scaled Euclidean solutions with compact solutions, generalizing existing initial data models in general relativity.

Findings

Constructed a one-parameter family of initial data with point-particle limits

Generalized Schwarzschild-de Sitter initial data

Extended IMP-type gluing theorems

Abstract

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits analogous to those of Gralla and Wald ("A rigorous derivation of gravitational self-force," Class. Quantum Grav. 2008). In particular, we produce examples of initial data which generalize Schwarzschild - de Sitter initial data and gluing theorems of IMP-type.