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

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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.

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Authors and Affiliations

  1. Simon Stevin Institute for Geometry, Wilhelminaweg 1, 2042 NN, Zandvoort, The Netherlands

    Stefan Haesen

  2. Department of Geometry and Topology, Universidad de Granada, 18071, Granada, Spain

    Miguel Ortega

Authors
  1. Stefan Haesen
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  2. Miguel Ortega
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Correspondence to Miguel Ortega.

Additional information

S. Haesen was partially supported by the Research Foundation—Flanders project G.0432.07. S. Haesen and M. Ortega were partially supported by the Spanish MEC Grant MTM2007-60731 with FEDER funds and the Junta de Andalucía Regional Grant P06-FQM-01951. This work was started when S. Haesen was a postdoctoral researcher at the Section of Geometry of the Katholieke Universiteit Leuven.

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Haesen, S., Ortega, M. Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group. Gen Relativ Gravit 41, 1819–1834 (2009). https://doi.org/10.1007/s10714-008-0754-x

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  • DOI: https://doi.org/10.1007/s10714-008-0754-x

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