Axial symmetry Type N space-time with a naked curvature singularity and Closed Time-like Curves

Abstract

A family of type N exact solution of the Einstein's field equations, regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, is present. The stress-energy tensor is of the anisotropic fluid coupled with pure radiation field satisfy the different energy conditions and the physical parameters diverge $r\to 0$. The space-time admitting a non-expanding, non-twisting, and shear-free geodesic null congruence and belongs to a special class of type N Kundt metrics. The space-time is geodesically complete along the radiation direction in the constant $z$-planes and exhibits geometrically different properties from the known pp-waves. The present family of solution admits closed time-like curves (CTC) which appear after a certain instant of time and the space-time is a four-dimensional generalization of the Misner space metric in curved space-time.

Typos corrected, accepted for publication in Gravitation and Cosmology

References in corpus (3)

• Extended time-travelling objects in Misner space
• Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities
• Black holes/naked singularities in four-dimensional non-static space-time and the energy-momentum distributions

Cited by in corpus (2)

• Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics
• Weyl Fermions in a Linear Class of Gödel-Type Space-Time Backgrounds