In this paper,we investigate Pseudo-Z symmetric space-timemanifolds. First, we deal with elementary properties showing that the associated form Ak is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of theWeyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS)4 spacetime; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Pseudo-Z symmetric space-times / C.A. Mantica, Y. Jin Suh. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 55:4(2014), pp. 042502.042502-1-042502.042502-12. [10.1063/1.4871442]
Pseudo-Z symmetric space-times
C.A. Mantica;
2014
Abstract
In this paper,we investigate Pseudo-Z symmetric space-timemanifolds. First, we deal with elementary properties showing that the associated form Ak is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of theWeyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS)4 spacetime; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.| File | Dimensione | Formato | |
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