부산대학교 도서관

A surface $S$ in the Minkowski spacetime $\Bbb{L}^4$ is calledtrapped when the mean curvature vector field $H$ is everywheretimelike. This kind of surface was introduced by Penrose whenconsidering singularity theorems in general relativity. If $H$ islightlike and nonzero in at least one point then $S$ is called marginally trapped. Finally, if $H$ is lightlike on a part of $S$and vanishes on another one, then $S$ is said to be partlymarginally trapped.\parOn the other hand, the inertial vacuum state of $\Bbb{L}^4$ is athermal state when analyzed regarding the notion of timetranslations defined by a one-parameter family of Lorentz boosts.The orbits of these boost isometries correspond to a family ofuniformly accelerating observers. This result, known as the Unruheffect, is actually a consequence of the fact that the Lorentz boostisometries possess a Killing horizon, i.e., a null surface which isnormal to the Killing field generating the isometries. Then theauthors consider the group $G$ of boost isometries to classify all$G$-invariant partly marginally trapped surfaces in $\Bbb{L}^4$.\parThis remarkable result yields a series of nice consequences. Forinstance, all $G$-invariant extremal surfaces in $\Bbb{L}^4$ lie in a totally geodesic $\Bbb{L}^3$. They also show thatthere exist no $G$-invariant extremal surfaces in $\Bbb{L}^4$with constant Gaussian curvature.\parThe paper is completed with a nice list of examples and an openproblem.