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.
Highlights
IntroductionWhere ρ is the radiation energy-density and kμ is the tangent vector field of geodesics null congruence
The energy-momentum tensor of radiation field [1] is given byTμν = ρ kμ kν, kμ kμ = 0, (1)where ρ is the radiation energy-density and kμ is the tangent vector field of geodesics null congruence
The studied metric is non-diverging (ρ = −(ω + i ) = 0), has a shear-free (σ = 0) geodesic null vector field which is considered the principal null direction aligned with radiative direction
Summary
Where ρ is the radiation energy-density and kμ is the tangent vector field of geodesics null congruence. The algebraically special (type II, D, III or N, conformally flat) non-twisting and shear-free pure radiation space-times with or without cosmological constant are known in literature For CTC space-time, the matter-energy sources must be realistic, that is, the stressenergy tensor must be known type of matter fields which satisfy the different energy conditions. Many known CTC space-time, for examples the traversable wormholes [18,19], and the warp drive models [20,21,22] violate the weak energy condition (WEC), which states that Tμν U μ U ν ≥ 0 for a time-like tangent vector field U μ, that is, the energy-density must be non-negative. The radiation field solutions in curved space-time without cosmological constant
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