A rigidity property of asymptotically simple spacetimes arising from conformally flat data

TL;DR

This paper proves that for certain vacuum Einstein spacetimes with conformally flat initial data, smooth extension through critical sets occurs only if the data is Schwarzschild near infinity, revealing a rigidity property.

Contribution

It establishes a rigidity result showing that smooth extensions at null infinity imply the initial data must be Schwarzschild near infinity.

Findings

Solutions extend smoothly only for Schwarzschild initial data.

Rigidity property links smoothness at null infinity to initial data form.

Characterizes conditions for regularity at spatial infinity in vacuum spacetimes.

Abstract

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.