https://doi.org/10.1140/epjc/s10052-018-5880-3
Regular Article - Theoretical Physics
A type N radiation field solution with 
in a curved space-time and closed time-like curves
Ajmal College of Arts and Science, Dhubri, Assam, 783324, India
* e-mail: faizuddinahmed15@gmail.com
Received:
20
February
2018
Accepted:
8
May
2018
Published online:
17
May
2018
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 non-expanding, 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.
© The Author(s), 2018
