Time machine in MTT-world (Q811377)

The time-machine property of a homogeneous Einstein-Maxwell spacetime [\textit{R. G. McLenaghan}, and \textit{N. Tariq}, J. Math. Phys. 16, No. 11, 2306-2312 (1975); and \textit{B. O. J. Tupper}, Gen. Relativity Gravitation 7, 479 (1976)] is disclosed. A method developed by the author [Sib. Math. J. 31, No. 3, 395-408 (1990); translation from Sib. Mat. Zh. 31, No. 3(181), 39-54 (1990; Zbl 0713.53035)], is applied on the basis of representation of the named spacetime as a Lie group \(M\) with a left- invariant Lorentzian metric. Left-shifts of a natural Lorentzian form for the corresponding Lie algebra to the whole of \(M\), yield the above MTT metric. A theorem is proved that the MTT spacetime admits a closed timelike worldline.