# On the Topology of Initial Data Sets with Higher Genus Ends

@article{Baker2014OnTT, title={On the Topology of Initial Data Sets with Higher Genus Ends}, author={Kenneth L. Baker and Gregory J. Galloway}, journal={Communications in Mathematical Physics}, year={2014}, volume={336}, pages={431-440} }

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…

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## References

SHOWING 1-10 OF 25 REFERENCES

### Essential closed surfaces in bounded 3-manifolds

- Mathematics
- 1997

A question dating back to Waldhausen [10] and discussed in various contexts by Thurston (see [9]) is the problem of the extent to which irreducible 3-manifolds with infinite fundamental group must…

### Topological censorship from the initial data point of view

- Mathematics
- 2012

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…

### On the Topology of Vacuum Spacetimes

- Mathematics
- 2003

Abstract. We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n + 1)-dimensions. We do this by gluing a solution of…

### Topological black holes: Outside looking in

- Physics
- 1997

I describe the general mathematical construction and physical picture of topological black holes, which are black holes whose event horizons are surfaces of non-trivial topology. The construction is…

### On 3-manifolds

- MathematicsGraduate Studies in Mathematics
- 2021

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P…

### Topological Censorship and Higher Genus Black Holes

- Mathematics
- 1999

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti‐de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such…

### Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons

- Physics
- 1997

We examine counterparts of the Reissner-Nordstr\"om\char21{}anti\char21{}de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface \ensuremath{\Sigma} of constant…

### The Area of Horizons and the Trapped Region

- Mathematics
- 2009

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally…

### Topological Censorship for Kaluza–Klein Space-Times

- Mathematics
- 2009

The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship…

### The Plateau problem for marginally outer trapped surfaces

- Mathematics
- 2007

We solve the Plateau problem for marginally outer trapped surfaces in general Cauchy data sets. We employ the Perron method and tools from geometric measure theory to force and control a blow-up of…