Black holes, marginally trapped surfaces and quasi-minimal surfaces

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Bang-Yen Chen


The concept of trapped surfaces introduced by Sir Roger Penrose in [Phys. Rev. Lett. 14 (1965), 57-59] plays an extremely important role in cosmology and general relativity. A black hole is a trapped region in a space-time enclosed by a marginally trapped surface. In term of mean curvature vector, a space-like surface in a space-time is marginally trapped if its mean curvature vector field is light-like at each point. In this article, we survey recent classification results on marginally trapped surfaces from differential geometric viewpoint. Also, we survey recent results on a closely related subject; namely, quasi-minimal surfaces in pseudo-Riemannian manifolds.

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How to Cite
Chen, B.-Y. (2009). Black holes, marginally trapped surfaces and quasi-minimal surfaces. Tamkang Journal of Mathematics, 40(4), 313–341.
Author Biography

Bang-Yen Chen

Department of Mathematics, Michigan State University, East Lansing, Michigan 48824--1027, U.S.A.