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Traversable Achronal Retrograde Domains In Spacetime

DOI: 10.1088/1361-6382/aa6549
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Benjamin Tippett at University of New Brunswick
Benjamin Tippett
David Tsang
David Tsang
David Tsang
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Abstract and Figures

There are many spacetime geometries in general relativity which contain closed timelike curves. A layperson might say that retrograde time travel is possible in such spacetimes. To date no one has discovered a spacetime geometry which emulates what a layperson would describe as a time machine. The purpose of this paper is to propose such a space-time geometry. In our geometry, a bubble of curvature travels along a closed trajectory. The inside of the bubble is Rindler spacetime, and the exterior is Minkowski spacetime. Accelerating observers inside of the bubble travel along closed timelike curves. The walls of the bubble are generated with matter which violates the classical energy conditions. We refer to such a bubble as a Traversable Achronal Retrograde Domain In Spacetime.
A schematic of the timelike observers confined to the interior and exterior of the bubble. Observers A (inside the bubble) and B (outside the bubble) experience the events in dramatically different ways. Arrows indicate the local arrow of time. Within the bubble, A will see the B’s events periodically evolve, and then reverse. Outside the bubble, observer B will see two versions of A emerge from the same location: one’s clock hands will turn clockwise, the other counterclockwise. The two versions of A will then accelerate towards one another and annihilate.
A schematic of the timelike observers confined to the interior and exterior of the bubble. Observers A (inside the bubble) and B (outside the bubble) experience the events in dramatically different ways. Arrows indicate the local arrow of time. Within the bubble, A will see the B’s events periodically evolve, and then reverse. Outside the bubble, observer B will see two versions of A emerge from the same location: one’s clock hands will turn clockwise, the other counterclockwise. The two versions of A will then accelerate towards one another and annihilate.
… 
Evolution of the boundaries of the bubble, as defined in section 2.1, as seen by an external observer. At T  =  −100 the bubble will suddenly appear, and split in to two pieces which will move away from one another (T=−75,T=−50). At T  =  0, the two bubbles will come to rest, and then begin accelerating towards one-another (T=+75,T=+50). Whereupon, at T  =  +100 the two bubbles will merge and disappear. (a) TARDIS boundaries at T  =  0. (b) TARDIS boundaries at T=±50. (c) TARDIS boundaries at T=±75. (d) TARDIS boundaries at T=±100.
Evolution of the boundaries of the bubble, as defined in section 2.1, as seen by an external observer. At T  =  −100 the bubble will suddenly appear, and split in to two pieces which will move away from one another (T=−75,T=−50). At T  =  0, the two bubbles will come to rest, and then begin accelerating towards one-another (T=+75,T=+50). Whereupon, at T  =  +100 the two bubbles will merge and disappear. (a) TARDIS boundaries at T  =  0. (b) TARDIS boundaries at T=±50. (c) TARDIS boundaries at T=±75. (d) TARDIS boundaries at T=±100.
… 
The light cones inside the bubble are meant to tip in a circular path relative to the exterior light cones. For illustrative purposes we have chosen to make counter-clockwise and upwards the ‘future’ directions in our diagram. This orientation is confirmed in the null curve diagram in figure 4.
The light cones inside the bubble are meant to tip in a circular path relative to the exterior light cones. For illustrative purposes we have chosen to make counter-clockwise and upwards the ‘future’ directions in our diagram. This orientation is confirmed in the null curve diagram in figure 4.
… 
Null geodesics travelling through a cross section y=0, z=0. The intersection of null curves can indicate the orientation of the light cone. The curves are colour coded according to the conformal infinities they extend towards. The red and green curves have both endpoints at the same respective conformal null infinity, while the blue ones stretch from one null infinity to the other.
Null geodesics travelling through a cross section y=0, z=0. The intersection of null curves can indicate the orientation of the light cone. The curves are colour coded according to the conformal infinities they extend towards. The red and green curves have both endpoints at the same respective conformal null infinity, while the blue ones stretch from one null infinity to the other.
… 
Tim has drawn a diagram, explaining his difficulties in setting up an initial value hypersurface and simulation. Two families of null curves in this diagram are ‘reflected’ by the bubble geometry. The red curves start and end at ‘past’ null infinity, causing them to intersect spacelike hypersurfaces in more than one place and forcing initial conditions placed on these surfaces will also need to satisfy additional consistency conditions. The green curves start and end at ‘future’ null infinity, bringing in new information which was not present on the initial hypersurface, and making predictions past the ‘Cauchy horizon’ impossible.
+1
Tim has drawn a diagram, explaining his difficulties in setting up an initial value hypersurface and simulation. Two families of null curves in this diagram are ‘reflected’ by the bubble geometry. The red curves start and end at ‘past’ null infinity, causing them to intersect spacelike hypersurfaces in more than one place and forcing initial conditions placed on these surfaces will also need to satisfy additional consistency conditions. The green curves start and end at ‘future’ null infinity, bringing in new information which was not present on the initial hypersurface, and making predictions past the ‘Cauchy horizon’ impossible.
… 
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1
Classical and Quantum Gravity
Traversable acausal retrograde
domains in spacetime
BenjaminKTippett1 and DavidTsang2
1 University of British Columbia, Okanagan, 3333 University Way,
Kelowna BC V1V 1V7, Canada
2 Center for Theory and Computation, Department of Astronomy, University
of Maryland, College Park, MD 20742, United States of America
E-mail: btippett@mail.ubc.ca and dtsang@astro.umd.edu
Received 24 August 2016, revised 8 March 2017
Accepted for publication 8 March 2017
Published 31 March 2017
Abstract
In this paper we present geometry which has been designed to t a layperson’s
description of a ‘time machine’. It is a box which allows those within it to
travel backwards and forwards through time and space, as interpreted by an
external observer. Timelike observers travel within the interior of a ‘bubble’
of geometry which moves along a circular, acausal trajectory through
spacetime. If certain timelike observers inside the bubble maintain a persistent
acceleration, their worldlines will close.
Our analysis includes a description of the causal structure of our spacetime,
as well as a discussion of its physicality. The inclusion of such a bubble in a
spacetime will render the background spacetime non-orientable, generating
additional consistency constraints for formulations of the initial value
problem. The spacetime geometry is geodesically incomplete, contains naked
singularities, and requires exotic matter.
Keywords: closed timelike curves, classical energy conditions,
naked singularities
(Some guresmay appear in colour only in the online journal)
1. Introduction
The possibility that some spacetime geometries permit retrograde time travel has long been a
preoccupation of both general relativists and popular ction [24]. Among physicists, General
Relativity’s allowance for closed timelike curves (CTCs) resulting from exotic spacetime
geometry is a subject of heated debate. While CTCs are—strictly speaking—a mathematical
possibility; they are philosophically undesirable. In a fashion similar to the debate over the
B K Tippett and D Tsang
Traversable acausal retrograde domains in spacetime
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Class. Quantum Grav.
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Class. Quantum Grav. 34 (2017) 095006 (12pp) https://doi.org/10.1088/1361-6382/aa6549
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