A type N radiation field solution with $$\Lambda <0$$ Λ < 0 in a curved space-time and closed time-like curves

Abstract

An anti-de Sitter background four-dimensional type N solution of the Einstein's field equations, is presented. The matter-energy content pure radiation field satisfies the null energy condition (NEC), and the metric is free-from curvature divergence. In addition, the metric admits a nonexpanding, non-twisting and shear-free geodesic null congruence which is not covariantly constant. The space-time admits closed time-like curves which appear after a certain instant of time in a causally well-behaved manner. Finally, the physical interpretation of the solution, based on the study of the equation of the geodesics deviation, is analyzed.

An axially symmetric spacetime with causality violation

“…It should be mentioned here that there are quite a number of causality violating solutions where there are no violations of the standard energy conditions of GR. A handful of such solutions would be the spacetimes discussed in [9,13,17,26,27]. The point of discussion here is that the violation of energy conditions is not a prerequisite for obtaining CTCs [9,28].…”

“…A family of Petrov type III solutions with a non-vanishing cosmological constant and aligned pure radiation field has been obtained in [34]. A few number of causality violating spacetimes with a pure radiation field as matter-energy content, with or without a cosmological constant or any fluid content, has been studied in [14,17,27,[35][36][37]. In [17] and [37], the studied spacetimes are of type II while the spacetimes in [14,27,35,36] belong to type N in the Petrov classification scheme.…”

“…A few number of causality violating spacetimes with a pure radiation field as matter-energy content, with or without a cosmological constant or any fluid content, has been studied in [14,17,27,[35][36][37]. In [17] and [37], the studied spacetimes are of type II while the spacetimes in [14,27,35,36] belong to type N in the Petrov classification scheme. The matter-energy content of the presented solution represents a pure radiation field in an asymptotically AdS spacetime.…”