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In this paper, we present a type D, non-vanishing cosmological constant,vacuum solution of the Einstein's field equations, extension of an axiallysymmetric, asymptotically flat vacuum metric with a curvature singularity. Thespace-time admits closed time-like curves (CTCs) that appear after a certaininstant of time from an initial spacelike hypersurface, indicating itrepresents a time-machine space-time. We wish to discuss the physicalproperties and show that this solution can be interpreted as gravitationalwaves of Coulomb-type propagate on anti-de Sitter space backgrounds. Ourtreatment focuses on the analysis of the equation of geodesic deviation.

advances in high energy physics

Axial symmetry cosmological constant vacuum solution of field equations  with a curvature singularity, closed time-like curves and deviation of  geodesics