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arXiv · 2109.08888

Marginal tubes and foliations by marginal surfaces

Pengyu Le
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Abstract

In this paper, we introduce the notion of a marginal tube, which is a hypersurface foliated by marginal surfaces. It generalises the notion of a marginally trapped tube and several notions of black hole horizons, for example trapping horizons, isolated horizons, dynamical horizons, etc. We prove that if every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null. There is no assumption on the topology of the marginal tube. To prove it, we study the geometry of spacelike surfaces in a 4-dimensional spacetime with the help of double null coordinate systems. The result is valid for arbitrary 4-dimensional spacetimes, regardless of any energy condition.

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Pengyu Le. 2021-09-18. Marginal tubes and foliations by marginal surfaces. https://doi.org/10.1088/1361-6382%2Fac571b

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