Extend Bartnik–Isenberg existence/uniqueness beyond spherical symmetry

Develop existence and uniqueness results for space-like dynamical horizon segments beyond spherical symmetry, extending Bartnik–Isenberg’s analysis, potentially by formulating the constraint equations on a DHS as an evolutionary system.

Background

The second law for DHSs follows from the Gauss–Codazzi constraints intrinsic to the horizon. In spherical symmetry, Bartnik and Isenberg solved the constraints and established existence and uniqueness for spherical DHSs, connecting area growth to fluxes.

A broader analysis beyond spherical symmetry would clarify the mathematical structure of DHSs (particularly space-like ones) and control their existence/uniqueness properties, which directly impacts numerical relativity and strong-field GR.