Topological censorship from the initial data point of view

2012/04/01 by Michael Eichmair, Eichmair, Michael, Gregory J. Galloway +3 · 1 voice · 3 citations
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.DG

paper · pdf · doi:10.48550/arxiv.1204.0278

arxiv published 2012/04/01 · arxiv updated 2013/06/16

Abstract

We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are diffeomorphic to R³. We establish a generalization of the Penrose singularity theorem which shows that the presence of an immersed marginally outer trapped surface generically implies the null geodesic incompleteness of any spacetime that satisfies the null energy condition and which admits a non-compact Cauchy surface. Taken together, these results can be viewed as an initial data version of the Gannon-Lee singularity theorem. The first result is a non-time-symmetric version of a theorem of Meeks-Simon-Yau which implies that every asymptotically flat Riemannian 3-manifold that is not diffeomorphic to R³ contains an embedded stable minimal surface. We also obtain an initial data version of the spacetime principle of topological censorship. Under physically natural assumptions, a 3-dimensional asymptotically flat initial data set with marginally outer trapped boundary and no immersed marginally outer trapped surfaces in its interior is diffeomorphic to R³ minus a finite number of open balls. An extension to higher dimensions is also discussed.

Cited by

• A simplified proof of a cosmological singularity theorem
• The Penrose singularity theorem, MOTS stability, and horizon topology in weighted spacetimes
• On the Chen-Teo family of stationary asymptotically locally Minkowskian black holes

Discussions

• Out of order, but this one is a misconception that influences other aspects of the question: In short: how do we consistently set up the initial data for something as conceptually simple as “three poi [stackexchange, 3 points]

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