Inflationary initial data for generic spatial topology

Morrow-Jones, Jonathan; Witt, Donald

doi:10.1103/physrevd.48.2516

Cited by 26 publications

(80 citation statements)

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“…In the locally spherically symmetric case, Morrow-Jones and Witt [6] have developed a method for getting a smooth gluing by taking into account a local deformation of the geometry in the direction orthogonal to the surface of symmetry.…”

Section: Summary and Discussionmentioning

confidence: 99%

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Thurston's geometrization conjecture and cosmological models

Yasuno¹,

Koike²,

Siino³

2001

Class. Quantum Grav.

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Abstract. We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurston's Geometrization Conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations. Such composite spacetimes are built from the spatially compact locally homogeneous vacuum spacetimes which have two commuting Killing vectors by gluing them through a timelike hypersurface admitting a homogeneous spatial slice spanned by the commuting Killing vectors. Topology of the spatial section of the timelike boundary is taken to be the torus. We also assume that the matter which will arise from the gluing is compressed on the boundary, i.e. we take the thin-shell approximation. By solving the junction conditions, we can see dynamical behavior of the connected (composite) spacetime. The Teichmüller deformation of the torus also can be obtained. We apply our formalism to a concrete model. The relation to the torus sum of 3-manifolds and the difficulty of this problem are also discussed.

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Section: Summary and Discussionmentioning

confidence: 99%

“…Morrow-Jones and Witt [6] studied about spacetimes with general topology by constructing the compact locally spherically symmetric 3-manifolds glued along twospheres, i.e. connected sum of 3-manifolds.…”

Section: Introductionmentioning

confidence: 99%

Thurston's geometrization conjecture and cosmological models

Yasuno¹,

Koike²,

Siino³

2001

Class. Quantum Grav.

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“…Again ∂ u is a local Killing vector field for this metric. Analyticity of these solutions in a coordinate chart follows immediately from their forms, (10) and (12). If in a given chart, a solution is in the Schwarzschild-de Sitter (anti-de Sitter) family with mass parameter M , then it cannot have a different mass parameter in any overlapping chart due to analyticity.…”

Section: Rpmentioning

confidence: 99%

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confidence: 99%

“…It is natural to consider its extension to other situations in gravitational physics. Birkhoff's theorem readily generalizes to the inclusion of electromagnetic fields [10], cosmological constant [8], with explicit exhibition of both the Schwarzschild-de Sitter and Nariai solutions in [11,12] (also in [13] without citation of previous references), and to other symmetry groups [14,15].2 Generalized Birkhoff's theorems have also been proven in lower and higher dimensions [16,17,18,19,20,21], certain alternate theories of gravity [22,23,24,25,26,27,28] including Lovelock gravity [29,30,31,32], and shown not to hold on Randall-Sundrum branes [33] and in some modified theories of gravity [34,35].Although Birkhoff's theorem is a classic result, many current textbooks and review articles on general relativity no longer provide a proof or even a careful statement of the theorem. Frequently it is cited as proving that the spherically symmetric vacuum solution is static.…”

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A simple proof of Birkhoff's theorem for cosmological constant

Schleich

Witt

2010

Journal of Mathematical Physics

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We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local Killing vector field.PACS numbers: 04.20.Cv, 04.20.Gz Birkhoff's theorem, that any spherically symmetric vacuum solution of Einstein's equations is locally isometric to a region in Schwarzschild spacetime, is not only a classic contribution to general relativity but is also an important tool in gravitational physics and cosmology. First proven for the vacuum Einstein equations, this theorem is traditionally credited to Birkhoff [1]; however it was recently rediscovered by Deser, when providing an alternate proof, that this theorem was published two years earlier by Jebsen [2,3,4]. (An english translation of Jebsen's paper with an introduction by Deser was published in General Relativity and Gravitation in 2005 [5, 6].) In older references, this theorem is credited as independently discovered by not only Birkhoff and Jebsen but also Alexandrow [7] and Eiesland [8].1 The multiple provenance of this theorem is a testament to its significance in general relativity. It is natural to consider its extension to other situations in gravitational physics. Birkhoff's theorem readily generalizes to the inclusion of electromagnetic fields [10], cosmological constant [8], with explicit exhibition of both the Schwarzschild-de Sitter and Nariai solutions in [11,12] (also in [13] without citation of previous references), and to other symmetry groups [14,15].2 Generalized Birkhoff's theorems have also been proven in lower and higher dimensions [16,17,18,19,20,21], certain alternate theories of gravity [22,23,24,25,26,27,28] including Lovelock gravity [29,30,31,32], and shown not to hold on Randall-Sundrum branes [33] and in some modified theories of gravity [34,35].Although Birkhoff's theorem is a classic result, many current textbooks and review articles on general relativity no longer provide a proof or even a careful statement of the theorem. Frequently it is cited as proving that the spherically symmetric vacuum solution is static. This is clearly not the case as recognized in many (but not all) proofs of the theorem (See, for example, the comment on Jebsen's proof in [36]). The interior region of the maximal analytic extension of Schwarzschild spacetime is not static; instead, it exhibits a spacelike Killing vector field. Of course, other regions of this spacetime do exhi...

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Topological censorship and chronology protection

Friedman¹,

Higuchi²

2006

Ann. Phys.

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Over the past two decades, substantial efforts have been made to understand the way in which physics enforces the ordinary topology and causal structure that we observe, from subnuclear to cosmological scales. We review the status of topological censorship and the topology of event horizons; chronology protection in classical and semiclassical gravity; and related progress in establishing quantum energy inequalities.Comment: Dedicated to Rafael Sorkin, whose tutoring and friendship from third grade on is responsible for one of us (JF) having spent his adult life in physics and whose work has inspired both of us. In v.2, some references are updated, and references are added to early work on 2+1 spacetimes and to work on event-horizon topolog

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Inflationary initial data for generic spatial topology

Cited by 26 publications

References 14 publications

Thurston's geometrization conjecture and cosmological models

Thurston's geometrization conjecture and cosmological models

A simple proof of Birkhoff's theorem for cosmological constant

Topological censorship and chronology protection

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