Closed spaces in cosmology

Fagundes, Helio V.

doi:10.1007/bf00756787

Cited by 34 publications

(26 citation statements)

References 21 publications

(24 reference statements)

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“…The last two types are the Heisenberg group and the solvable Lie group. These types are anisotropic geometries and one can write an explicit metric for them [25]. However, it is not clear whether any of these last three types can be realized as a supersymmetric 3-cycle.…”

Section: Three Manifoldsmentioning

confidence: 99%

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Supergravity and D-branes wrapping supersymmetric 3-cycles

Nieder

2001

J. High Energy Phys.

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We construct dual supergravity descriptions of D3-branes wrapping associative 3-cycles L. We analyse the conditions for having five-dimensional background solutions of the form AdS 2 × L and show that they require L to be of constant negative curvature type. This provides AdS 2 background solutions when L is the hyperbolic space H 3 or its quotients by subgroups of its isometry group. We construct a regular numerical solution interpolating between AdS 5 in the UV and AdS 2 × H 3 in the IR. The IR fixed point exists at the "intersection" of the Coulomb and Higgs branches. We analyse the singular supergravity solutions which correspond to moving into the Higgs and the Coulomb branches. For negative constant curvature spaces the singularity is of a "good" type in the Higgs branch and of a "bad" type in the Coulomb branch. For positive constant curvature spaces such as S 3 the singularity is of a "bad" type in both the Higgs and the Coulomb branches. We discuss the meaning of these results.

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Section: Three Manifoldsmentioning

confidence: 99%

“…In order to satisfy equation (25) with the boundary condition (36) ϕ has to approach a constant value in the far IR (r → ∞). Equation (37) then also requires e 2g to be asymptotically constant.…”

Section: Ads 2 × L Solutionsmentioning

confidence: 99%

Supergravity and D-branes wrapping supersymmetric 3-cycles

Nieder

2001

J. High Energy Phys.

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“…D. Closed spaces in cosmology [9] This paper improves on the previous one, and discusses the question of local vs. global homogeneity of the constant curvature models.…”

Section: B Compactification Of Friedmann's Hyperbolicmentioning

confidence: 94%

Exploring the global topology of the universe

Fagundes¹

2002

Braz. J. Phys.

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“…where SL(2, R) is the universal covering of SL(2, R). In [45] it was shown that there exists a correspondence, not necessarily one to one, between the nine Bianchi cosmologies and the eight Thurston model geometries, which is summarized in table 1. 10 In the following, we list explicitely the metrics for solvegeometry/VI −1 and nilgeometry/II in terms of G-invariant one-forms θ A , as well as the nonvanishing structure constants of the related Lie algebras.…”

Section: Jhep12(2019)151mentioning

confidence: 99%

Black holes in Sol minore

Faedo

Farotti

Klemm

2019

J. High Energ. Phys.

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We consider black holes in five-dimensional N = 2 U(1)-gauged supergravity coupled to vector multiplets, with horizons that are homogeneous but not isotropic. We write down the equations of motion for electric and magnetic ansätze, and solve them explicitely for the case of pure gauged supergravity with magnetic U(1) field strength and Sol horizon. The thermodynamics of the resulting solution, which exhibits anisotropic scaling, is discussed. If the horizon is compactified, the geometry approaches asymptotically a torus bundle over AdS 3. Furthermore, we prove a no-go theorem that states the nonexistence of supersymmetric, static, Sol-invariant, electrically or magnetically charged solutions with spatial cross-sections modelled on solvegeometry. Finally, we study the attractor mechanism for extremal static non-BPS black holes with nil-or solvegeometry horizons. It turns out that there are no such attractors for purely electric field strengths, while in the magnetic case there are attractor geometries, where the values of the scalar fields on the horizon are computed by extremization of an effective potential V eff , which contains the charges as well as the scalar potential of the gauged supergravity theory. The entropy density of the extremal black hole is then given by the value of V eff in the extremum.

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Closed spaces in cosmology

Cited by 34 publications

References 21 publications

Supergravity and D-branes wrapping supersymmetric 3-cycles

Supergravity and D-branes wrapping supersymmetric 3-cycles

Exploring the global topology of the universe

Black holes in Sol minore

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