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Classical and Quantum Gravity

Traversable acausal retrograde

domains in spacetime

BenjaminKTippett1 and DavidTsang2

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 guresmay 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

Printed in the UK

095006

CQGRDG

© 2017 IOP Publishing Ltd

34

Class. Quantum Grav.

CQG

1361-6382

10.1088/1361-6382/aa6549

Paper

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Classical and Quantum Gravity

IOP

2017

1361-6382 /17/095006+12$33.00 © 2017 IOP Publishing Ltd Printed in the UK

Class. Quantum Grav. 34 (2017) 095006 (12pp) https://doi.org/10.1088/1361-6382/aa6549