Projective collineations in spacetimes

Hall, Graham; Lonie, D. P.

doi:10.1088/0264-9381/12/4/010

Cited by 36 publications

(70 citation statements)

References 19 publications

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“…Here one can clearly see that the space-time (37) which admits proper special projective collineation is a special class of static spherically symmetric space-time. We know from [2,5] …”

Section: Case (Ii)mentioning

confidence: 99%

“…The aim of this paper is to find the existance of proper projective collineation in non-static spherically symmetric space-times. Different approaches [1][2][3][4][5][6][7][8][9][10][11][12] were adopted to study projective collineations. In this paper an approach, which basically consists of some algebraic and direct integration techniques, is developed to study the projective collineation for the above space-times.…”

Section: Introductionmentioning

confidence: 99%

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Proper Curvature Collineations in Nonstatic Spherically Symmetric Space–times

Ramzan

2008

Int. J. Mod. Phys. A

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“…Here one can clearly see that the space-time (37) which admits proper special projective collineation is a special class of static spherically symmetric space-time. We know from [2,5] …”

Section: Case (Ii)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Proper Curvature Collineations in Nonstatic Spherically Symmetric Space–times

Ramzan

2008

Int. J. Mod. Phys. A

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“…Some techniques for studying projective symmetry in general relativity theory were developed by the present authors in [1,2]. That study was heavily based on the algebraic structure of the curvature tensor and included an account of the relationship between the existence of (proper) projective symmetry in a space-time and the latter's holonomy type.…”

Section: Introductionmentioning

confidence: 99%

“…A more natural and elegant account of this relationship will be given here. To avoid undue repetition, the results in [1] will be used regularly here as will those dealing with space-time holonomy theory in [4,5].…”

Section: Introductionmentioning

confidence: 99%

Holonomy and projective symmetry in spacetimes

Hall¹,

Lonie²

2004

Class. Quantum Grav.

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“…Thus, it is possible to use all the machinery of Lie group theory as it has been largely done for example with isometries in order to find, classify and study solutions of four-dimensional Einstein's field equations [51]. Similar analyses have been performed for conformal motions, affine collineations, linear collineations and conformal collineations (see [54,2,26,27,28,15,29,51] and references therein) with perhaps a less firmly established physical interpretation. An account of the classical symmetries studied in General Relativity can be found in [38,51].…”

Section: Introductionmentioning

confidence: 99%

General study and basic properties of causal symmetries

Gómez-Lobo¹,

Senovilla²

2003

Class. Quantum Grav.

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Abstract. We fully develop the concept of causal symmetry introduced in [21]. A causal symmetry is a transformation of a Lorentzian manifold (V, g) which maps every future-directed vector onto a future-directed vector.We prove that the set of all causal symmetries is not a group under the usual composition operation but a submonoid of the diffeomorphism group of V . Therefore, the infinitesimal generating vector fields of causal symmetriescausal-preserving vector fields-are associated to local one-parameter groups of transformations which are causal symmetries only for positive values of the parameter -one-parameter submonoids of causal symmetries-. The pullback of the metric under each causal symmetry results in a new rank-2 future tensor, and we prove that there is always a set of null directions canonical to the causal symmetry. As a result of this it makes sense to classify causal symmetries according to the number of independent canonical null directions. This classification is maintained at the infinitesimal level where we find the necessary and sufficient conditions for a vector field to be causal preserving. They involve the Lie derivatives of the metric tensor and of the canonical null directions. In addition, we prove a stability property of these equations under the repeated application of the Lie operator. Monotonicity properties, constants of motion and conserved currents can be defined or built using casual preserving vector fields. Some illustrative examples are presented.

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Projective collineations in spacetimes

Cited by 36 publications

References 19 publications

Proper Curvature Collineations in Nonstatic Spherically Symmetric Space–times

Proper Curvature Collineations in Nonstatic Spherically Symmetric Space–times

Holonomy and projective symmetry in spacetimes

General study and basic properties of causal symmetries

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