A Cylindrically Symmetric and Static Anisotropic Fluid Spacetime and the Naked Singularity

Faizuddin Ahmed,Farook Rahaman

doi:10.1155/2018/7839619

A Cylindrically Symmetric and Static Anisotropic Fluid Spacetime and the Naked Singularity

Faizuddin Ahmed, Farook Rahaman

Open Access

https://doi.org/10.1155/2018/7839619

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Abstract

A cylindrically symmetric and static solution of Einstein’s field equations was presented. The spacetime is conformally flat and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The matter-energy source anisotropic fluids violate the weak energy condition (WEC) and diverge on the symmetry axis. We discuss geodesics motion of free test-particles near to the singularity, geodesic expansion in the metric to understand the nature of singularity which is naked or covered, and finally the C-energy of the spacetime.

Highlights

Investigation of the nature of singularities in gravitational collapse solution of Einstein’s field equations in different systems is of particular interest in general relativity
Thorne proposed a hoop conjecture [22] concerning the formation of black holes in cylindrical symmetric system
We considered static fluid distributions; there are only three kinematic variables, namely, the expansion Θ, the acceleration vector Uμ, and the shear tensor σμ] associated with the fluid four-velocity vector which are defined by

Summary

Introduction

Investigation of the nature of singularities in gravitational collapse solution of Einstein’s field equations in different systems is of particular interest in general relativity. The study of gravitational collapse in spherically symmetric spacetime has led to many examples of naked singularities (e.g., [1, 2], see [3, 4] and references therein). Some other nonspherical gravitational collapse model possesses a naked singularity (e.g., [19,20,21]). A cylindrical symmetric and static solution of the field equations possessing a naked curvature singularity on the symmetry axis, satisfying the strong curvature condition, will be presented. We have relaxed the Darmois conditions, and the presented solution is a special case of the very well-known static, cylindrically symmetric, and conformally flat solutions [23] (see [24])

Conformally Flat Nonvacuum Spacetime

Kr dKr dλ

Conclusions