Closed Timelike Curves and Time Travel: Dispelling the Myth

G?del’s contention that closed timelike curves (CTC’s) are a necessary consequence of the Einstein equations for his metric is challenged. It is seen that the imposition of periodicity in a timelike coordinate is the actual source of CTC’s rather than the physics of general relativity. This conclusion is supported by the creation of G?del-like CTC’s in flat space by the correct choice of coordinate system and identifications. Thus, the indications are that the notion of a time machine remains exclusively an aspect of science fiction fantasy. The element of the identification of spacetime points is also seen to be the essential factor in the modern creation of CTC’s in the Gott model of moving cosmic strings.     

Computers with Closed Timelike Curves Can Solve Hard Problems Efficiently

A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for the problem of factoring large numbers and argue that a similar approach can solve NP-complete and PSPACE-complete problems. I discuss the potential impact of quantum effects on this result.     

A twist in the geometry of rotating black holes: seeking the cause of acausality

We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is opposite to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this.     

A comment on Bonnor–Steadman closed timelike curves

The existence and stability closed timelike curves in a Bonnor–Ward spacetime without torsion line singularities is shown by exhibiting particular examples.     

The Decay of Massive Scalar Field in Non-Static Gödel Type Universe with Viscous Fluid and Heat Flow

In this study, we have investigated the dynamics of non-static Gödel type rotating universe with massive scalar field, viscous fluid and heat flow in the presence of cosmological constant. For various cosmic matter forms, the behavior of the cosmological constant (Λ), shear (η) and bulk (ξ) viscosity coefficients and other kinematic quantities have studied in the early universe. We have showed the decay of massive scalar field in the non-static rotating Gödel type universe and we have obtained constant scalar field with and without source density. Also, we have investigated the effects of massive scalar field on the matter density and pressure. From solutions of the field equations, we have a cosmological model with non-zero expansion, shear, heat flux and rotation. Also some physical and geometrical aspects of the model discussed.     

Closed time-like curves in flat Lorentz space–times

We consider the region of closed time-like curves (CTCs) in three-dimensional flat Lorentz space–times. The interest in this global geometrical feature goes beyond the purely mathematical one. Such space–times are lower-dimensional toy models of sourceless Einstein gravity or cosmology. In three dimensions all such space–times are known: they are quotients of Minkowski space by a suitable group of Poincaré isometries. The presence of CTCs would indicate the possibility of “time machines”, a region of space–time where an object can travel along in time and revisit the same event. Such space–times also provide a testbed for the chronology protection conjecture, which suggests that quantum back reaction would eliminate CTCs. In particular, our interest in this note will be to find the set free of CTCs for , where is modeled on Minkowski space and γ is a Poincaré transformation. We describe the set free of CTCs where γ is hyperbolic, parabolic, and elliptic.     

Gödel Kink Spacetime

A 2+1 version of a rotating perfect fluid spacetime of Gödel type is examined to see whether it has a Finkelstein-Misner kink. It is shown, by three different methods, that the kink number is one.     

Tri-Hamiltonian Toda Lattice and a Canonical Bracket for Closed Discrete Curves

Flows on (or variations of) discrete curves in give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierarchy. Here it is shown that the canonical symplectic structure on , which can be interpreted as the phase space of closed discrete curves in with length N, induces Poisson commutation relations on the above-mentioned subalgebra which yield the tri-Hamiltonian poisson structure of the Toda lattice hierarchy.     

Quantum CTC's in General Relativity

We review different spacetimes that contain nonchronal regions separated from the causal regions by chronology horizons and investigate their connection with some important aspects one would expect to be present in a final theory of quantum gravity, including: stability to classical and quantum metric fluctuations, boundary conditions of the universe and gravitational topological defects corresponding to spacetime kinks.     

On the Local Structure of the Klein–Gordon Field on Curved Spacetimes

This paper investigates wave equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave equation vanishing in an open set vanishes in the envelope of this set, which may be considerably larger and in the case of timelike tubes may even coincide with the spacetime itself. We apply this result to the real scalar field on a globally hyperbolic spacetime and show that the field algebra of an open set and its envelope coincide. As an example, there holds an analog of Borchers' timelike tube theorem for such scalar fields and, hence, algebras associated with world lines can be explicitly given. Our result applies to cosmologically relevant spacetimes.     

Interpreting Quantum Interference Using a Berry’s Phase-like Quantity

We show that quantum interference can be interpreted in terms of a phase invariant quantity, not unlike the Berry’s phase. Under this interpretation, closed loops in time become fundamental quantum entities, and all quantum states become periodic. Decoherence is then seen to occur naturally as a consequence. This formalism, although counterintuitive, provides another useful way of assigning meaning to quantum probabilities and quasi-probabilities.     

Gödel type metrics in Einstein–aether theory

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field is introduced to the theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the Gödel type of metrics of general relativity are also exact solutions of the Einstein–aether theory. The only field equations are the 3D Maxwell field equations and the parameters are left free except c ₁ ? c ₃ = 1.