A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation

Abstract

We present a topologically trivial, non-vacuum solution of the Einstein's field equations in four-dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid p = ω ρ. The metric admits a twisting, shearfree, non-exapnding timelike geodesic congruence. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.

Spin-0 system of DKP equation in the background of a flat class of Gödel-type spacetime

“…Consider the following stationary space-time [24] (see Refs. [23,25,26]) in the coordinates (t, x, y, z) given by…”

The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

“…Consider the following stationary space-time [103] (see also Refs. [64,65]) in the coordinates (x 0 = t, x 1 = x, x 2 = y, x 3 = z) given by (11) where α 0 > 0 is a real number, and the function H (x) = α 0 x and D(x) = 1.…”

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

“…The next one is the van Stockum space-time [2], which predates the Gödel solution and was shown later to have CTCs [3]. Examples of space-time admitting CTCs including NUT-Taub metric [4][5][6][7], Kerr and Kerr-Newman black hole solution [8][9][10], Gott time-machine [11], Grant space-time [12], Krasnikov tube [13], Bonnor's metrics [14][15][16][17][18][19], and others [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Space-time with causality violating curves is classified as either eternal or true time-machine spacetimes.…”

“…In this category would be [1] or [2] (see also, Refs. [23,25,27,32,36]). A true time machine space-time is the one in which CTCs evolve at a particular instant of time from an initial space-like hypersurface in a causally well-behaved manner satisfying all the energy conditions with known type of matter fields.…”