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On the Topology of Initial Data Sets with Higher Genus Ends

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Abstract

In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets that contain no (immersed) marginally outer trapped surfaces in their interior must have simple topology: they are a product of a surface and an interval, or a mild variation thereof, depending on the connectedness of the horizon and on its genus relative to that of the end. The results obtained here extend results in Eichmair et al. (J Differ Geom 95:389–405, 2013) to the case of higher genus ends.

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Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Kenneth L. Baker & Gregory J. Galloway

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  1. Kenneth L. Baker
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  2. Gregory J. Galloway
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Correspondence to Gregory J. Galloway.

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Communicated by P. T. Chruściel

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Baker, K.L., Galloway, G.J. On the Topology of Initial Data Sets with Higher Genus Ends. Commun. Math. Phys. 336, 431–440 (2015). https://doi.org/10.1007/s00220-015-2309-9

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  • DOI: https://doi.org/10.1007/s00220-015-2309-9

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