Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine

Abstract

We present a gravitational collapse null dust solution of the Einstein field equations. The space-time is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near the singularity and the gravitational lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that this solution depends on the local gravitational field consisting of two components with amplitudes Ψ 2 and Ψ 4 .

Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

“…In order to analyze the effect of local gravitational fields of these solutions, we have used the equations of geodesic deviation [25,33,52,[63][64][65][66] which in terms of orthonormal frame e ðaÞ are…”

“…Thus, the presented metrics as well as the one studied in [51] evolve CTC from an initial space-like hypersurface at a certain instant of time. Though causality violating space-times have been studied extensively in the literature, few of them belongs to true time-machine space-time (e.g., [24-26, 28, 31, 33, 34, 37]), and others in (e.g., [26,[51][52][53]) are lacking one or more basic requirements for a true time-machine space-time. In addition, many time-machine models mentioned in the introduction violate one or more the energy condition.…”

“…[11,12]). In addition, there is a curvature singularity in some solutions admitting CTCs [3,35,[48][49][50][51][52][53].…”

High Speed Cylindrical Gravitational Collapse with Anisotropic Pressure

“…Cylindrical symmetric gravitational collapse of counter rotating dust shells can be found in the [16,17], axially symmetric vacuum solution [18], and cylindrical symmetric collapse in anisotropic in [7]. An axially symmetric null dust gravitational collapse has been discussed in [19]. The non-spherical gravitational collapse has been discussed in [20][21][22].…”

Осесимметричное Пространство-Время Чистого Излучения С Геодезическими, Нарушающими Причинность

“…Геодезические -это мировые линии свободных частиц. Пространство-время машины времени из работ [13], [14] нарушает слабое энергетическое условие и/или в нем присутствует сингулярность кривизны [15].…”