Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime
Peibiao Zhao, Uday Chand De, B\"ulent \"Unal, Krishnendu De
TL;DR
This paper investigates conditions under which pseudosymmetric spacetimes can be characterized as perfect fluid spacetimes, establishing key geometric and physical relationships and providing explicit examples.
Contribution
It proves that pseudosymmetric generalized Robertson-Walker spacetimes are perfect fluids and that conformally flat pseudosymmetric spacetimes are generalized Robertson-Walker, with additional results on dust fluids and examples.
Findings
Pseudosymmetric generalized Robertson-Walker spacetimes are perfect fluids.
Conformally flat pseudosymmetric spacetimes are generalized Robertson-Walker.
Pseudosymmetric dust fluids with constant scalar curvature are vacuum.
Abstract
The aim of the present paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson-Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein's field equations without cosmological constant is vacuum. Finally, we construct a non-trivial example of pseudosymmetric spacetime.
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