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

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.

37 pages

References in corpus (4)

• On de Sitter-like and Minkowski-like space-times
• Asymptotic properties of the development of conformally flat data near spatial infinity
• The Maxwell field on the Schwarzschild spacetime: behaviour near spatial infinity
• On smoothness-asymmetric null infinities

Cited by in corpus (8)

• Asymptotic simplicity and static data
• The Maxwell-scalar field system near spatial infinity
• Conformal structures of static vacuum data
• On the smoothness of the critical sets of the cylinder at spatial infinity in vacuum spacetimes
• Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
• Staticity and regularity for zero rest-mass fields near spatial infinity on flat spacetime
• Explorations of the infinite regions of space-time
• Valiente Kroon's obstructions to smoothness at infinity