Many solutions of Einstein's field equations contain closed timelike curves (CTC). Some of these solutions refer to ordinary materials in situations which might occur in the laboratory, or in astrophysics. It is argued that, in default of a reasonable interpretation of CTC, general relativity does not give a satisfactory account of all phenomena within its terms of reference. PACS number 0420 I...

We describe the time evolution of quantum systems in a classical background spacetime by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve C is interpreted as the time evolution operator of an observer moving along C. The holonomy group of the connection, which can be viewed as a group of local symmetry...

What is the shape of space in a spacetime? One way of addressing this issue is to consider edgeless spacelike submanifolds of the spacetime. An alternative is to foliate the spacetime by timelike curves and consider the quotient obtained by identifying points on the same timelike curve. In this article we investigate each of these notions and obtain conditions such that it yields a meaningful s...

The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x0 and x1, with x1 in the chronological future of x0, and a ratio q/m, it is proved that a timelike connecting solution of the Lorentz force equation exists provided there is no null connecting geodesics and the spacetime is glo...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

In this work, we deal with a classical differential geometry topic in Minkowski space-time. First, we prove that there are no timelike involutes of a time-like evolute. In the light of this result, we observed that involute curve transforms to a time-like curve when evolute is a space-like helix with a time-like principal normal. Then, we investigated relationships among Frenet-Serret apparatus...

A quantum field Φ(x) exists at an event x ∈ M of space-time (M, g) in general only as a quadratic form Φ(x). Only after smearing Φ(x) with a smooth test function f we get an operator Φ(f). In this paper the question is considered whether it is possible as well to smear Φ(x) with a singular test function T (i.e. test distributions) supported by a smooth timelike curve γ. It is shown that this is...

The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x0 and x1, with x1 in the chronological future of x0, and a ratio q/m, it is proved that a timelike connecting solution of the Lorentz force equation exists provided there is no null connecting geodesic and the spacetime is glob...