| 1. |
- Goliath, Martin, et al.
(författare)
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Spatially self-similar spherically symmetric perfect-fluid models
- 1998
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 15:1, s. 167-186
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Tidskriftsartikel (refereegranskat)abstract
- Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems
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| 2. |
- Goliath, Martin, et al.
(författare)
-
Timelike self-similar spherically symmetric perfect-fluid models
- 1998
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 15:9, s. 2841-2863
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Tidskriftsartikel (refereegranskat)abstract
- Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems
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| 3. |
- Nilsson, Ulf S., et al.
(författare)
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Hypersurface homogeneous and hypersurface self-similar models
- 1997
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 14:7, s. 1965-1989
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Tidskriftsartikel (refereegranskat)abstract
- Dynamical systems for hypersurface homogeneous and hypersurface self-similar models with non-null symmetry surfaces are derived. The equations are cast in a geometric form based on properties of the symmetry surfaces that emphasize the close connection between the various models. Perfect fluid models are discussed in particular. It is shown how the models form a hierarchical structure where simpler models act as building blocks for more complicated ones. Expressions for the fluid's kinematic properties are given and discussed in the context of various special cases.
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| 4. |
- Nilsson, Ulf S., et al.
(författare)
-
Rigidly rotating stationary cylindrically symmetric perfect fluid models
- 1997
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 14:10, s. 2931-2945
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Tidskriftsartikel (refereegranskat)abstract
- Einstein's field equations for rigidly rotating stationary Bianchi type I models are investigated, focusing on the cylindrically symmetric cases. The equations are rewritten as a first-order system of autonomous ordinary differential equations and dimensionless variables are introduced such that the reduced phase space is compact. The system is then studied qualitatively using the theory of dynamical systems. The cylindrically symmetric submanifold is studied in detail.
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| 5. |
- Nilsson, Ulf, et al.
(författare)
-
Spatially self-similar locally rotationally symmetric perfect fluid models
- 1996
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 13:6, s. 1601-1622
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Tidskriftsartikel (refereegranskat)abstract
- Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first-order system of autonomous ordinary differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of differential equations is reduced as far as possible. The system is subsequently analysed qualitatively for some of the models. The nature of the singularities occurring in the models is discussed
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| 6. |
- Uggla, Claes, et al.
(författare)
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Classifying Einstein's field equations with applications to cosmology and astrophysics
- 1995
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 12:10, s. 2525-2548
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Tidskriftsartikel (refereegranskat)abstract
- The field equations for spacetimes with finite-dimensional Hamiltonian dynamics are discussed. Examples of models belonging to this class are the cosmological spatially homogeneous models, the astrophysically interesting static spherically symmetric models, static cylindrically symmetric models, and certain cosmological self-similar models. A number of different sources are considered. Although these models arise from quite different physical contexts, their field equations all share a common mathematical structure. This motivates a classification of Einstein's field equations. Several classification schemes, based on properties under various variable transformations, are presented. It is shown how these schemes can be used to classify dynamical properties of the models and how one can thereby obtain qualitative information. It is also shown how one scheme can be used in order to find symmetries and exact solutions.
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| 7. |
- van Elst, Henk, et al.
(författare)
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General relativistic 1 + 3 orthonormal frame approach
- 1997
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 14:9, s. 2673-2695
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Tidskriftsartikel (refereegranskat)abstract
- The dynamical equations of an extended 1 + 3 orthonormal frame approach to the relativistic description of spacetime geometries are explicitly presented and discussed in detail. In particular, the Bianchi identities for the Weyl curvature tensor occur in a fully expanded form, as they are given a central role in the extended formalism. It is shown how one can naturally introduce local coordinates, both in the 1 + 3 threading and the ADM 3 + 1 slicing context. By specializing the general 1 + 3 dynamical equations it is demonstrated how a number of problems of interest can be obtained. In particular, the simplest choices of spatial frames for spatially homogeneous cosmological models, locally rotationally symmetric spacetime geometries, cosmological models with an Abelian isometry group G2 and 'silent' dust cosmological models are discussed.
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| 8. |
- van Elst, Henk, et al.
(författare)
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Integrability of irrotational silent cosmological models
- 1997
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 14:5, s. 1151-1162
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Tidskriftsartikel (refereegranskat)abstract
- We revisit the issue of integrability conditions for the irrolational silent cosmological models. We formulate the problem both in 1 + 3 covariant and 1 + 3 orthonormal frame notation and show that there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearized silent models, but not in the general exact nonlinear case. Thus there is a linearization instability and it is highly unlikely that there is a large class of silent models We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I and indicate further issues that await clarification.
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| 9. |
- DEMKIN, P
(författare)
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ON THE STABILITY OF P-BRANE
- 1995
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Ingår i: CLASSICAL AND QUANTUM GRAVITY. - : IOP PUBLISHING LTD. - 0264-9381. ; 12:2, s. 289-296
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Stability of some solutions of the equations of motion of bosonic p-branes in curved and flat spacetimes is stated.
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