Extension to non-axisymmetric data

Develop a rigorous definition of angular momentum for non-axisymmetric asymptotically flat initial data that enables an extension of the Angular Momentum Penrose Inequality beyond axisymmetry.

Background

The proof and inequality in the paper rely on axisymmetry to define and conserve Komar angular momentum along the AMO flow. Without a Killing field, quasi-local angular momentum lacks a canonical definition compatible with the presented method.

Extending the inequality to non-axisymmetric settings would require a viable generalization of angular momentum that interacts correctly with the geometric and analytic framework underpinning the Jang–conformal–AMO approach.