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… 

On static Poincar\'e-Einstein metrics

The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are

Existence of CMC Cauchy surfaces from a spacetime curvature condition

In this note we present a result establishing the existence of a compact CMC Cauchy surface from a curvature condition related to the strong energy condition.

Roads to topological censorship

In this note we review some aspects of topological censorship. We present several (actually five) alternative sets of hypotheses which allow the proof of a topological censorship theorem for

On static Poincaré-Einstein metrics

The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are

References

SHOWING 1-10 OF 25 REFERENCES

Essential closed surfaces in bounded 3-manifolds

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

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

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

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

  • S. Nikitin
  • Mathematics
    Graduate 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

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

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

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

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

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