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تسجيل مستخدم جديدSome remarks on a new exotic spacetime for time travel by free fall
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Davide Fermi
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This work is essentially a review of a new spacetime model with closed causal curves, recently presented in another paper (Class. Quantum Grav. textbf{35}(16) (2018), 165003). The spacetime at issue is topologically trivial, free of curvature singularities, and even time and space orientable. Besides summarizing previous results on causal geodesics, tidal accelerations and violations of the energy conditions, here redshift/blueshift effects and the Hawking-Ellis classification of the stress-energy tensor are examined.
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Inspired by some recent works of Tippett-Tsang and Mallary-Khanna-Price, we present a new spacetime model containing closed timelike curves (CTCs). This model is obtained postulating an ad hoc Lorentzian metric on $mathbb{R}^4$, which differs from th
e Minkowski metric only inside a spacetime region bounded by two concentric tori. The resulting spacetime is topologically trivial, free of curvature singularities and is both time and space orientable; besides, the inner region enclosed by the smaller torus is flat and displays geodesic CTCs. Our model shares some similarities with the time machine of Ori and Soen but it has the advantage of a higher symmetry in the metric, allowing for the explicit computation of a class of geodesics. The most remarkable feature emerging from this computation is the presence of future-oriented timelike geodesics starting from a point in the outer Minkowskian region, moving to the inner spacetime region with CTCs, and then returning to the initial spatial position at an earlier time; this means that time travel to the past can be performed by free fall across our time machine. The amount of time travelled into the past is determined quantitatively; this amount can be made arbitrarily large keeping non-large the proper duration of the travel. An important drawback of the model is the violation of the classical energy conditions, a common feature of many time machines. Other problems emerge from our computations of the required (negative) energy densities and of the tidal accelerations; these are small only if the time machine is gigantic.
These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institutes Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal tr
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