Curvature properties of a special type of pure radiation metrics

JOURNAL OF GEOMETRY AND PHYSICS

卷:136

Article

Shaikh, Absos Ali¹  Kundu, Haradhan¹  Ali, Musavvir²  Ahsan, Zafar³ 

[1] Univ Burdwan, Dept Math, Burdwan 713104, W Bengal, India

[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[3] Univ Islamic Sci, Fac Sci & Technol, Nilai, Malaysia

关键词: Pure radiation metric;    pp-wave metric;    Einstein field equation;    Semisymmetric type curvature conditions;    Pseudosymmetric type curvature conditions;    quasi-Einstein manifold;   

DOI  :  10.1016/j.geomphys.2018.11.002

来源: Elsevier

【 摘 要 】

A spacetime denotes a pure radiation field if its energy-momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989 Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a vacuum spacetime. In the present paper we investigate the curvature properties of the pure radiation metrics presented by Ludwig and Edgar. It is shown that such a pure radiation spacetime is semisymmetric, Ricci simple, R-space by Venzi and its Ricci tensor is Riemann compatible. It is also proved that its conformal curvature 2-forms and Ricci 1-forms are recurrent. We also present a pure radiation type metric and evaluate its curvature properties along with the form of its energy-momentum tensor. It is interesting to note that such a pure radiation type metric is Ein(3) and 3-quasi-Einstein. We also find out the sufficient conditions for which this metric represents a generalized pp-wave, pure radiation and perfect fluid. Finally we made a comparison between the curvature properties of Ludwig and Edgar's pure radiation metric and pp-wave metrics. (C) 2018 Elsevier B.V. All rights reserved.

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