On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes

TL;DR

This paper proves that stationary vacuum spacetimes with angular momentum cannot have conformally flat, maximal Cauchy slices, highlighting fundamental geometric restrictions in general relativity.

Contribution

It establishes the nonexistence of conformally flat slices in Kerr and similar spacetimes, using asymptotic analysis and properties of null infinity.

Findings

No conformally flat, maximal slices in Kerr spacetime

Bowen-York data cannot develop smooth null infinity

Stationary solutions admit smooth null infinity

Abstract

It is proved that a stationary solutions to the vacuum Einstein field equations with non-vanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and non-boosted. The proof is based on results coming from a certain type of asymptotic expansions near null and spatial infinity --which also show that the developments of Bowen-York type of data cannot have a development admitting a smooth null infinity--, and from the fact that stationary solutions do admit a smooth null infinity.