Dain's invariant on non-time symmetric initial data sets

Abstract

We extend Dain's construction of a geometric invariant characterising static initial data sets for the vacuum Einstein field equations to situations with a non-vanishing extrinsic curvature. This invariant gives a measure of how much the initial data sets deviates from stationarity. In particular, it vanishes if and only if the initial data set is stationary. Thus, the invariant provides a quantification of the amount of gravitational radiation contained in the initial data set.

References in corpus (3)

• On the construction of a geometric invariant measuring the deviation from Kerr data
• Killing spinor initial data sets
• KIDs prefer special cones

Cited by in corpus (5)

• Non-stationary Energy in General Relativity
• Dain's invariant for black hole initial data
• Non-stationary Energy of Perfect Fluid Sources in General Relativity
• Bowen-York Model Solution Redux
• Constraints and Time Evolution in Generic $f$(Riemann) Gravity