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A Study of Spacetimes with vanishing M−projective Curvature Tensor

Authors

Kaushik Chattopadhyay, Arindam Bhattacharyya and Dipankar Debnath

Abstract

In this paper we study about the M−projectively flat perfect fluid spacetime. First of all we showed that the Riemannian curvature tensor of an M−projectively flat spacetime is covariantly constant. Then we found the length of the Ricci operator in an M−projectively flat perfect fluid spacetime
and proved that the isotropic pressure and entry density of an M−projectively
flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant are constant. Then we showed that an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant and obeying the timelike convergence condition has positive isotropic pressure. Further we showed that the isotropic pressure and the energy density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant vanishes in a purely electromagnetic distribution. Lastly we showed that an M−projectively flat perfect fluid spacetime with the energy momentum tensor of an electromagnetic field such that the spacetimesatisfies Einsteins field equation without cosmological constant is a Euclidean space

Keywords and Phrases : M−projectively flat perfect fluid spacetime, Riemannian curvature tensor, purely electromagnetic distribution
AMS Subject Classification : : Primary 53C25; Secondary 53D10, 53C44

Received date : July 24, 2018

Accepted date: October 11, 2018

cited by: J.T.S. Vol. 12 (2018), pp.23-31

 

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