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Formation of closed timelike curves in a composite vacuum/dust asymptotically flat spacetime

“…The Energy conditions are all satisfied if ǫ ≥ 0 and u α is a timelike vector. The system (8), along with the initial data on S, uniquely determine the evolution of geometry (and matter) throughout D + (S) [9][26].…”

“…Thus, Godel's rotating-dust cosmological model [1] violates conditions (i,ii), as does Tipler's rotating-string solution [2]; the wormhole model by Moris, Thorne and Yurtsever [3] violates condition (iii). Gott's solution [4] of two infinitely long cosmic strings violates condition (ii) [10], and Mallett's solution [8] violates condition (i) (see [11]). …”

Can a Circulating Light Beam Produce a Time Machine

“…Thus, e.g., the metric obtained in Ref. [1] in the limit = w = 0 has, from Eq. (I-20), the metric component f = g 00 proportional to ρ rather than the expected Minkowski result f = −1.…”

“…The solution obtained in Ref. [1] has the remarkable property that in the region exterior to the cylinder a plane of constant z contains circular closed timelike curves (CTC's) enclosing the cylinder of all radii ρ > ρ min > ρ 0 , where ρ 0 is the radius of the cylinder. The CTC's occur even if becomes arbitrarily small, although in the limit → 0, ρ min , the minimum radius of the CTC's, → ∞.…”

“…[1] from the ansatz ξ = constant differs from the metric of conventional cylindrical coordinates only by a coordinate transformation. We will, however, see presently that the situation is more complex than that.…”