Asymptotic simplicity and static data

Abstract

The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions to the regular finite initial value problem at spatial infinity for this class of initial data sets extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data sets coincide with static data in a neighbourhood of infinity. This result highlights the special role played by static data among the class of initial data sets for the Einstein field equations whose development gives rise to a spacetime with a smooth conformal compactification at null infinity.

25 pages

References in corpus (1)

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

Cited by in corpus (7)

• The Maxwell-scalar field system near spatial infinity
• Conformal structures of static vacuum data
• 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
• Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: Nonspherical Schwarzschild waves and singularities at null infinity
• Explorations of the infinite regions of space-time
• Conformal extensions for stationary spacetimes