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TMF, 2018, Volume 195, Number 1, Pages 117–129 (Mi tmf9359)  

This article is cited in 3 scientific papers (total in 3 papers)

Conformal collineations of the Ricci and energy–momentum tensors in static plane symmetric space–times

S. S. Akhtara, T. Hussaina, A. H. Bokharib, F. Khana

a Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan
b Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

Abstract: We provide a complete classification of static plane symmetric space–times according to conformal Ricci collineations {(}CRCs{\rm)} and conformal matter collineations (CMCs) in both the degenerate and nondegenerate cases. In the case of a nondegenerate Ricci tensor, we find a general form of the vector field generating CRCs in terms of unknown functions of $t$ and $x$ subject to some integrability conditions. We then solve the integrability conditions in different cases depending upon the nature of the Ricci tensor and conclude that the static plane symmetric space–times have a $7$-, $10$- or $15$-dimensional Lie algebra of CRCs. Moreover, we find that these space–times admit an infinite number of CRCs if the Ricci tensor is degenerate. We use a similar procedure to study CMCs in the case of a degenerate or nondegenerate matter tensor. We obtain the exact form of some static plane symmetric space–time metrics that admit nontrivial CRCs and CMCs. Finally, we present some physical applications of our obtained results by considering a perfect fluid as a source of the energy–momentum tensor.

Keywords: conformal Ricci collineation, conformal matter collineation, Ricci collineation, matter collineation.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9359

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English version:
Theoretical and Mathematical Physics, 2018, 195:1, 595–606

Bibliographic databases:

PACS: 04.20.Jb
Received: 21.02.2017

Citation: S. S. Akhtar, T. Hussain, A. H. Bokhari, F. Khan, “Conformal collineations of the Ricci and energy–momentum tensors in static plane symmetric space–times”, TMF, 195:1 (2018), 117–129; Theoret. and Math. Phys., 195:1 (2018), 595–606

Citation in format AMSBIB
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\paper Conformal collineations of the~Ricci and energy--momentum tensors in static plane symmetric space--times
\jour TMF
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\pages 117--129
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\pages 595--606
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hussain T., Akhtar S.S., “Energy Conditions and Conservation Laws in Ltb Metric Via Noether Symmetries”, Eur. Phys. J. C, 78:8 (2018), 677  crossref  isi
    2. Akhtar S.S., Hussain T., Bokhari A.H., “Positive Energy Condition and Conservation Laws in Kantowski-Sachs Spacetime Via Noether Symmetries”, Symmetry-Basel, 10:12 (2018), 712  crossref  isi
    3. Akhtar S.S., Hussain T., “Energy Conditions and Conservation Laws in Lrs Bianchi Type i Spacetimes Via Noether Symmetries”, Commun. Theor. Phys., 71:3 (2019), 298–306  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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