Study of a new class of cylindrically symmetric space-time in general relativity

Abstract

A new class of solutions of Einstein field equations is investigated for a cylindrically symmetric spacetime when the source of gravitation is a perfect fluid. To get the deterministic solution a relation between metric coefficients A = (BC) n is assumed. Certain physical and geometric properties of the model are also discussed.

A new class of relativistic perfect fluid cylinders with expansion proportional to shear scalar

“…In order to obtain such solutions we assumed metric potentials in separable form. All the solutions obtained are new and different than those obtained by Kandalkar and Gawande (2008). Solutions due to Kandalkar and Gawande (2008) for perfect fluids seem to be erroneous as they do not satisfy the isotropic conditions (G 1 1 = G 2 2 = G 3 3 ).…”

“…Kandalkar and Gawande (2008) Case (ii) in their paper can be obtained taking α 1 = 1 in the above case and it can easily be observed that the solution in their article is not fully correct. …”

“…A = (BC) n . We could show that all the solutions obtained by Kandalkar and Gawande (2008) are erroneous as they do not satisfy the isotropy conditions.…”

“…Recently, Baysal et al (2001), Kilinc and Yavuz (2007) have studied cosmological models in cylindrically symmetric inhomogeneous universe in the presence string. Pradhan et al (2007) have obtained a new class of solutions of inhomogeneous nonlinear cylindrically symmetric cosmological model when the source of gravitation is a string.…”

“…Pradhan et al (2007) have obtained a new class of solutions of inhomogeneous nonlinear cylindrically symmetric cosmological model when the source of gravitation is a string. However, Kandalkar and Gawande (2008) obtained some perfect fluid solutions taking the expansion proportional to the eigen value of shear tensor which is in fact equivalent to A = (BC) n where A = g 11 = g 44 , B = g 22 and C = g 33 of the cylindrically symmetric Einstein-Rosen metric.…”