학술논문

Boost invariant marginally trapped surfaces in Minkowski 4-space.
Document Type
Journal
Author
Haesen, S. (B-KUL) AMS Author Profile; Ortega, M. (E-GRAN-G) AMS Author Profile
Source
Classical and Quantum Gravity (Classical Quantum Gravity) (20070101), 24, no. 22, 5441-5452. ISSN: 0264-9381 (print).eISSN: 1361-6382.
Subject
53 Differential geometry -- 53C Global differential geometry
  53C80 Applications to physics
Language
English
Abstract
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.