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

## TL;DR

This paper presents a new exact solution to Einstein's equations in anti-de Sitter space with a pure radiation field, featuring closed time-like curves and a well-behaved causal structure, with implications for understanding spacetime geometry.

## Contribution

It introduces a novel type N solution with negative cosmological constant that admits closed time-like curves and satisfies the null energy condition, expanding the class of known exact solutions.

## Key findings

- The solution is free from curvature divergence.
- It admits closed time-like curves appearing causally well-behaved.
- The physical interpretation is supported by geodesic deviation analysis.

## 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 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.