Recurrence metrics and the physics of closed time-like curves (original) (raw)

A new argument for the non-existence of Closed Timelike Curves

In this paper, we attempt to present a short argument, different from that of the original proofs by that of Hawking, for a theorem stated that no closed timelike curves can exist. In a later paper, we apply this to quantum gravity and relate the curvature of spacetime to this theorem. Also, we present this paper as a preliminary introduction to the complete argument of this, and we also provide a preliminary notion of the concepts which will be narrated in the later papers. We also use this as a starting basis for a true theory of everything for a theory of everything. We use the notation of [1] and of .

Closed Timelike Curves and Time Travel: Dispelling the Myth

Foundations of Physics, 2005

Gödel'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 Gödel-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.

Closed timelike geodesics in a gas of cosmic strings

2008

We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.

Stability of closed timelike curves in the Gödel universe

General Relativity and Gravitation, 2007

We study, in some detail, the linear stability of closed timelike curves in the Gödel universe. We show that these curves are stable. We present a simple extension (deformation) of the Gödel metric that contains a class of closed timelike curves similar to the ones associated to the original metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in the Gödel universe with or without the inclusion of regular or exotic matter are stable under linear perturbations. We also find a sort of structural stability.

Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection

Universe, 2021

I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to “save” the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and...

Closed timelike smooth curves in the general theory of relativity

1975

For a space-time which admits a closed timelike smooth curve it is estimatedthat~" ~2 9 10-24 9 ~p l 2, where 9 is the real time and l the spatial length associated with the timelike curve, and p is the density of material. In connection with Howard's paper [i] dealing with the cosmological model of C~del [2] and particularly with GSdel's statement that a closed timelike smooth curve exists in his model, it is important to reconsider this interesting problem in the general theory of relativity. Howard casts some doubt on the result of Chandrasekhar and Wright [3] that a closed timelike smooth geodesic is impossible in the GSdel model. It is shown below that the original conclusion in [3] is correct. Different opinions have been expressed about models which admit closed timelike smooth curves (timelike eycles)(see [5]; [8]; [6], p. 625. The estimates which we make below, however, show that the phenomena either cannot be observed in practice, or are only realized in areas where modern physics has not yet penetrated, or must be considered from, say, a quantum-mechanical rather than a classical point of view. Let { I i}mi =1 (m >-1), the intervals containing the zeroes of the function f~' (t), be so small that

Identification of a Gravitational Arrow of Time!!!, PHYSICAL REVIEW LETTERS October 2014

It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an "arrow of time." We show that this is not so. The simplest nontrivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian N-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each, a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as "records." Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of the records of one branch and deduce a unique past and future direction from inspection of the available records.

A Gravitational Origin of the Arrows of Time

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the 'past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The 'paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.

Time, Closed Timelike Curves and Causality

2002

General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. These apparently violate causality, producing time-travel paradoxes. We shall briefly discuss these geometries and analyze some of their physical aspects.