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Curvature properties of Robinson–Trautman metric

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Abstract

The curvature properties of Robinson–Trautman metric have been investigated. It is shown that Robinson–Trautman metric is a Roter type metric, and in a consequence, admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Moreover, it is proved that this metric is a 2-quasi-Einstein, the Ricci tensor is Riemann compatible and its Weyl conformal curvature 2-forms are recurrent. It is also shown that the energy momentum tensor of the metric is pseudosymmetric and the conditions under which such tensor is of Codazzi type and cyclic parallel have been investigated. Finally, we have made a comparison between the curvature properties of Robinson–Trautman metric and Som–Raychaudhuri metric.

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Acknowledgements

The authors wish to express their sincere thanks to the referee for his valuable suggestions towards the improvement of the work. This work initially started in Department of Mathematics, Aligarh Muslim University when the first author A. A. Shaikh was working there as a professor. The algebraic computations of Section 3, 4 and 5 are performed by a computer program in Wolfram Mathematica.

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Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, 713104, India

    Absos Ali Shaikh

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, 202002, India

    Musavvir Ali

  3. Faculty of Science and Technology, University of Islamic Sciences, Nilai, Malaysia

    Zafar Ahsan

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  1. Absos Ali Shaikh
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  2. Musavvir Ali
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  3. Zafar Ahsan
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Shaikh, A.A., Ali, M. & Ahsan, Z. Curvature properties of Robinson–Trautman metric. J. Geom. 109, 38 (2018). https://doi.org/10.1007/s00022-018-0443-1

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