Corvino's construction using Brill waves

TL;DR

This paper explores using Brill waves in Corvino's construction to glue Schwarzschild ends in two-black-hole initial data, aiming to reduce spurious gravitational radiation.

Contribution

It introduces a novel approach of employing Brill waves in Corvino's gluing method and analyzes its effectiveness in lowering gravitational energy.

Findings

Positive first-order reduction in energy via this method

Potential to decrease spurious gravitational radiation

Feasibility of using Brill waves in initial data construction

Abstract

For two-black-hole time-symmetric initial data we consider the Corvino construction of gluing an exact Schwarzschild end. We propose to do this by using Brill waves. We address the question of whether this method can be used to reduce the overall energy, which seems to relate to the question of whether it can reduce the amount of `spurious' gravitational radiation. We find a positive answer at first order in the inverse gluing radius.