Global Properties of Warped Solutions in General Relativity

Katanaev, M. O.; Klösch, Thomas; Kummer, Wolfgang

doi:10.1006/aphy.1999.5923

Cited by 37 publications

(53 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As already mentioned the pseudo-Schwarzschild metric (2) is locally the only so (2, 1)-invariant solution of the Einstein field equations in the vacuum ‡ . This is the static solution found in [12] and also, in the context of warped solutions, in [10]. The more physically interesting gravitational field, generated by a distribution of matter described by an energy-momentum tensor T µν and reducing in the vacuum to the previous one, is given by…”

mentioning

confidence: 54%

On SO(2, 1) symmetry in general relativity

Vilasi¹,

Vitale²

2002

Class. Quantum Grav.

View full text Add to dashboard Cite

The role of the SO(2, 1) symmetry in General Relativity is analyzed. Cosmological solutions of Einstein field equations invariant with respect to a space-like Lie algebra Gr, with 3 ≤ r ≤ 6 and containing so(2, 1) as a subalgebra, are also classified.PACS numbers: 04.20.-q, 02.20.-a, 98.80.-k Gravitational models are usually classified in terms of their group of isometries, namely the number of Killing vectors, the values of the structure constants and the transitivity regions, i.e. the regions on which the isometry group acts transitively. The classification of all non-isomorphic isometry groups is a well known and solved issue in the context of Group Theory; for instance, there exist 9 non-isomorphic 3 -dimensional groups, G 3 , which yield the so-called Bianchi models.A simpler, but important, example is provided by the G 2 groups. In this case the corresponding Lie algebra G 2 is described in terms of two Killing vectors X, Y satisfying the commutation relation [X, Y ] = sY with s = 0, 1, this corresponding respectively to the Abelian and non-Abelian case.Interesting gravitational fields are represented by metrics possessing a higher degree of symmetry (for an exhaustive review on the various classifications of such models available in the literature see for example [11]). Among them particular attention have attracted homogeneous or hypersurface-homogeneous models like the Friedmann-Robertson-Walker metric (FRW) which is G 6 -symmetric, 1

show abstract

mentioning

confidence: 54%

On SO(2, 1) symmetry in general relativity

Vilasi¹,

Vitale²

2002

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…where K = 1, 0, −1 for spherical, planar, or hyperbolic reductions, respectively [33]. Λ is the four-dimensional cosmological constant, and κ > 0 is the inverse gravitational constant in four dimensions.…”

Section: The Actionmentioning

confidence: 99%

Effective Action for Scalar Fields in Two-Dimensional Gravity

Katanaev

2002

Annals of Physics

Self Cite

View full text Add to dashboard Cite

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.

show abstract

“…It can be shown that its variation leads to the same EOM as the ones from the original 4D action when the symmetry is introduced there. This point is nontrivial as witnessed by the reduced action resulting from warped metrics in Einstein gravity [16]. From the Gowdy line-element alone it is not clear why to define as dilaton fields X and Y as in (15).…”

Section: Gowdy Modelmentioning

confidence: 99%

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

2001

Self Cite

View full text Add to dashboard Cite

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories, and cosmology many models contain more than just one scalar field (e.g. inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g. dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g. spherically reduced Scalar-Tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.

show abstract

Global Properties of Warped Solutions in General Relativity

Cited by 37 publications

References 19 publications

On SO(2, 1) symmetry in general relativity

On SO(2, 1) symmetry in general relativity

Effective Action for Scalar Fields in Two-Dimensional Gravity

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Contact Info

Product

Resources

About