부산대학교 도서관

A surface $S$ in the Minkowski spacetime $\Bbb{L}^4$ is called trapped when the mean curvature vector field $H$ is everywhere timelike. This kind of surface was introduced by Penrose when considering singularity theorems in general relativity. If $H$ is lightlike 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 partly marginally trapped. \par On the other hand, the inertial vacuum state of $\Bbb{L}^4$ is a thermal state when analyzed regarding the notion of time translations defined by a one-parameter family of Lorentz boosts. The orbits of these boost isometries correspond to a family of uniformly accelerating observers. This result, known as the Unruh effect, is actually a consequence of the fact that the Lorentz boost isometries possess a Killing horizon, i.e., a null surface which is normal to the Killing field generating the isometries. Then the authors consider the group $G$ of boost isometries to classify all $G$-invariant partly marginally trapped surfaces in $\Bbb{L}^4$. \par This remarkable result yields a series of nice consequences. For instance, all $G$-invariant extremal surfaces in $\Bbb{L}^4$ lie in a totally geodesic $\Bbb{L}^3$. They also show that there exist no $G$-invariant extremal surfaces in $\Bbb{L}^4$ with constant Gaussian curvature. \par The paper is completed with a nice list of examples and an open problem.