Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group

TL;DR

This paper classifies spacelike surfaces in Minkowski 4-space invariant under spacelike rotations, focusing on those with lightlike or zero mean curvature, and explores their Gaussian curvature and construction methods.

Contribution

It provides a local classification of such surfaces, including marginally trapped surfaces, and introduces a method to assemble these surfaces with prescribed curvature properties.

Findings

Classification of invariant surfaces with lightlike or zero mean curvature

Existence results for surfaces with prescribed Gaussian curvature

A gluing procedure for constructing complex surfaces

Abstract

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector field vanishes. In particular, a local description of marginally trapped surfaces invariant under spacelike rotations is exhibited.