On the theory of homothetic and affine orbits in space time

Graham Stanley Hall; M. T. Patel

doi:10.1088/0264-9381/21/19/015

On the theory of homothetic and affine orbits in space time

Graham Stanley Hall, M. T. Patel

Mathematical Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Following recent work on the theory of Killing orbits in spacetime [1], an extension of these ideas is made to include the orbits of the homothetic and affine Lie algebras of symmetry vector fields. The possibility of a coincidence of orbits from the Killing, homothetic or affine algebras is explored and the results related to the stability of the orbits. A classification of homothetic isotropy is given and several examples of the possible orbit and isotropy behaviour are presented.

Original language	English
Pages (from-to)	4731-4742
Number of pages	11
Journal	Classical and Quantum Gravity
Volume	21
Issue number	19
DOIs	https://doi.org/10.1088/0264-9381/21/19/015
Publication status	Published - 2004

Keywords

FIXED-POINTS
CONFORMAL-SYMMETRIES
TIME
COLLINEATIONS

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10.1088/0264-9381/21/19/015

Cite this

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title = "On the theory of homothetic and affine orbits in space time",

abstract = "Following recent work on the theory of Killing orbits in spacetime [1], an extension of these ideas is made to include the orbits of the homothetic and affine Lie algebras of symmetry vector fields. The possibility of a coincidence of orbits from the Killing, homothetic or affine algebras is explored and the results related to the stability of the orbits. A classification of homothetic isotropy is given and several examples of the possible orbit and isotropy behaviour are presented.",

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author = "Hall, {Graham Stanley} and Patel, {M. T.}",

year = "2004",

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AU - Hall, Graham Stanley

AU - Patel, M. T.

PY - 2004

Y1 - 2004

N2 - Following recent work on the theory of Killing orbits in spacetime [1], an extension of these ideas is made to include the orbits of the homothetic and affine Lie algebras of symmetry vector fields. The possibility of a coincidence of orbits from the Killing, homothetic or affine algebras is explored and the results related to the stability of the orbits. A classification of homothetic isotropy is given and several examples of the possible orbit and isotropy behaviour are presented.

AB - Following recent work on the theory of Killing orbits in spacetime [1], an extension of these ideas is made to include the orbits of the homothetic and affine Lie algebras of symmetry vector fields. The possibility of a coincidence of orbits from the Killing, homothetic or affine algebras is explored and the results related to the stability of the orbits. A classification of homothetic isotropy is given and several examples of the possible orbit and isotropy behaviour are presented.

KW - FIXED-POINTS

KW - CONFORMAL-SYMMETRIES

KW - TIME

KW - COLLINEATIONS

U2 - 10.1088/0264-9381/21/19/015

DO - 10.1088/0264-9381/21/19/015

M3 - Article

SN - 0264-9381

VL - 21

SP - 4731

EP - 4742

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 19

ER -

On the theory of homothetic and affine orbits in space time

Abstract

Keywords

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