Construction of hyperboloidal initial data

TL;DR

This paper discusses a method for constructing hyperboloidal initial data in general relativity, focusing on the conformal approach and conditions for regularity, along with a brief overview of Einstein evolution equations in unphysical spacetime.

Contribution

It introduces a conformal method for hyperboloidal initial data construction and details conditions for regularity of solutions at the boundary.

Findings

Conditions for regularity of solutions are identified.

The conformal method effectively constructs hyperboloidal initial data.

Brief overview of Einstein evolution equations in unphysical setting.

Abstract

I describe the conformal method for constructing solutions of the hyperboloidal constraint equations as well as the conditions needed on the free data in order to have regularity up to boundary for the solutions to the constraint equations. A brief discussion of the Einstein evolution equations in the unphysical setting is given.