‎the object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎at first we prove that a quasi-conformally flat spacetime is einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎einstein's field equation with cosmological constant is covariant constant‎. ‎next‎, ‎we prove that if the perfect...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic. PACS 04.20.Jb, 98.80.Hw

The spacetime geometry on the equatorial slice through a Kerr black hole is formally equivalent to the geometry felt by phonons entrained in a rotating fluid vortex. We analyse this example of “analogue gravity” in some detail: First, we find the most general acoustic geometry compatible with the fluid dynamic equations in a collapsing/expanding perfect-fluid line vortex. Second, we demonstrate...

The aim of the present paper is to obtain condition under which a pseudosymmetric spacetime be perfect fluid spacetime. It proven that generalized Robertson-Walker Moreover, we establish conformally flat Next, it shown dust with constant scalar curvature satisfying Einstein's field equations without cosmological vacuum. Finally, construct non-trivial example

Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as “minimally” curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three parameter family of perfect f...

We present a class of singularity free exact cosmological solutions of Einstein’s equations describing a perfect fluid with heat flow. It is obtained as generalization of the Senovilla class [1] corresponding to incoherent radiation field. The spacetime is cylindrically symmetric and globally regular. PACS numbers : 04.20 Jb, 98.80 Dr † E-mail address : [email protected] 1 Senovilla [1] has...

Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star — a static spherically symmetric blob of fluid with position-independent density — the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the...