Boost invariant marginally trapped surfaces in Minkowski 4-space

TL;DR

This paper classifies boost-invariant extremal and partly marginally trapped surfaces in Minkowski 4-space, showing non-existence of certain extremal surfaces with constant Gaussian curvature and providing a method to construct new trapped surfaces.

Contribution

It introduces a classification of boost-invariant extremal and partly marginally trapped surfaces and presents a construction method for new trapped surfaces in Minkowski 4-space.

Findings

No extremal boost-invariant surfaces with constant Gaussian curvature exist.

A procedure to construct partly marginally trapped surfaces by gluing is provided.

A proper star-surface is explicitly constructed.

Abstract

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invariant under the group of boost isometries. As an application, a proper star-surface is constructed.