Kerr Initial data

TL;DR

This paper derives conditions on vacuum initial data using the Mars-Simon tensor to identify when its evolution matches a Kerr spacetime, expressed via a scalar function's vanishing.

Contribution

It introduces a new scalar function criterion on initial data that guarantees development into a Kerr spacetime, advancing the understanding of Kerr initial data characterization.

Findings

Conditions for Kerr spacetime development derived from initial data.

Scalar function on initial hypersurface must vanish for Kerr isometry.

Applications of the conditions discussed in the context of spacetime analysis.

Abstract

Exploiting a 3+1 analysis of the Mars-Simon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of a positive scalar function defined on the initial data hypersurface. Applications of this result are discussed.