Killing equations | ScienceGate

In this paper, conformal motions are studied in plane symmetric static space–times. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these space–times are presented. All possibilities for the existence of conformal motions in these space–times are exhausted.

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AUTOMATIC SYMMETRY INVESTIGATION OF SPACE-TIME METRICS

International Journal of Modern Physics D ◽

10.1142/s0218271894000551 ◽

1994 ◽

Vol 03 (01) ◽

pp. 323-326 ◽

Cited By ~ 5

Author(s):

THOMAS WOLF ◽

GUY GREBOT

Keyword(s):

Lie Algebra ◽

Computer Algebra ◽

Space Time ◽

Killing Equations

Computer algebra programs, [Formula: see text] and [Formula: see text] for automatically formulating and solving Killing equations and calculating the corresponding Lie algebra are described and examples are given.

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Structures of conserved currents and mass spectra for scalar fields. III. Current classification scheme in terms of Killing equations and the Goldstone theorem

Canadian Journal of Physics ◽

10.1139/p81-223 ◽

1981 ◽

Vol 59 (11) ◽

pp. 1680-1681

Author(s):

Meiun Shintani

Keyword(s):

Mass Spectra ◽

Classification Scheme ◽

Goldstone Boson ◽

Scalar Fields ◽

Conformal Transformations ◽

Goldstone Theorem ◽

Scalar Particles ◽

Conformally Invariant ◽

Conserved Currents ◽

Killing Equations

We present a new classification scheme for the currents Jμ(x) = Qμν(x)Cν(x) in terms of the solutions of the Killing equations for Cμ(x). The new scheme enables us to treat any coordinate transformations (e.g., special conformal transformations), and to discuss the mass spectra for the scalar particles in a conformally-invariant system. Moreover, with the aid of the generalized Goldstone theorem exploited in the previous article under the same title, we shall point out the nonexistence of the Goldstone boson with regard to the special conformal transformations.

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Conformal vector fields of Bianchi type-I spacetimes

Modern Physics Letters A ◽

10.1142/s0217732321502540 ◽

2021 ◽

Author(s):

Suhail Khan ◽

Maria Bukhari ◽

Ali H. Alkhaldi ◽

Akram Ali

Keyword(s):

Vector Fields ◽

Bianchi Type ◽

Conformal Killing ◽

Type I ◽

Bianchi Type I ◽

Conformal Vector ◽

Conformal Vector Fields ◽

Integration Techniques ◽

Metric Functions ◽

Killing Equations

This paper aims to investigate Conformal Vector Fields (CVFs) of Bianchi type-I spacetimes. A set of 10-coupled Partial Differential Equations (PDEs) is obtained from the conformal Killing equations. These equations are solved by using direct integration techniques to explore the components of CVFs. Utilizing these components, we get a system of three integrability conditions. Finally, we achieve CVFs along with conformal factors for unique possibilities of unknown metric functions from the solution of these conditions. From our results, it is examined that Bianchi type-I spacetimes admit five or fifteen CVFs for specific choices of metric functions.

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Killing Equations in the Space R5

Deformed Spacetime ◽

10.1007/978-1-4020-6283-4_21 ◽

2007 ◽

pp. 303-312

Keyword(s):

Killing Equations

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Chapter 3 Generalized Killing Equations

Mathematics in Science and Engineering - Invariant Variational Principles ◽

10.1016/s0076-5392(08)61832-9 ◽

1977 ◽

pp. 51-61

Keyword(s):

Killing Equations

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Pseudo null curve variations for Bishop frame in 3D semi-Riemannian manifold

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500439 ◽

2019 ◽

Vol 16 (03) ◽

pp. 1950043 ◽

Cited By ~ 1

Author(s):

Zehra Özdemi̇r

Keyword(s):

Magnetic Field ◽

Riemannian Manifold ◽

Riemannian Manifolds ◽

Vector Fields ◽

Space Form ◽

Charged Particles ◽

Null Curve ◽

Null Curves ◽

The Magnetic Field ◽

Killing Equations

In the present paper, the relation between invariants of the pseudo null curves and the variational vector fields of semi-Riemannian manifolds is introduced. After that, the Killing equations are written in terms of the Bishop curvatures along the pseudo null curve. By means of this approach, Killing equations make allow to interpret the movement of charged particles within the magnetic field. Afterwards, as an application, pseudo null magnetic curves are defined using the Killing variational vector field. The parametric representations of all pseudo null magnetic curves are determined in semi-Riemannian space form. Moreover, various examples of pseudo null magnetic curves are illustrated.

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