Book contents
- Frontmatter
- Contents
- Contributors
- Symposium Program
- Papers from both Volumes Classified by Subject
- Preface
- Charles W. Misner: Insight and Discovery
- Remarks Concerning the Geometries of Gravity and Gauge Fields
- Gravity and Unification of Fundamental Interactions
- Minisuperspaces: Symmetries and Quantization
- Quantum Cosmology
- A Pictorial History of some Gravitational Instantons
- No Time Machines from Lightlike Sources in 2+1 Gravity
- Inhomogeneity and Anisotropy Generation in FRW Cosmologies
- Misner, Kinks and Black Holes
- The Quantum Mechanics of Closed Systems
- Cosmological Vacuum Phase Transitions
- Minisuperspace as a Quantum Open System
- Ricci Flow on Minisuperspaces and the Geometry-Topology Problem
- Classical and Quantum Dynamics of Black Hole Interiors
- Matter Time in Canonical Quantum Gravity
- The Isotropy and Homogeneity of the Universe
- Recent Advances in ADM Reduction
- Some Progress in Classical Canonical Gravity
- Harmonic Map Formulation of Colliding Electrovac Plane Waves
- Geometry, the Renormalization Group and Gravity
- An Example of Indeterminacy in the Time-Development of “Already Unified Field Theory”: A Collision between Electomagnetic Plane Waves
- Non-static Metrics of Hiscock-Gott Type
- Non-Standard Phase Space Variables, Quantization and Path-Integrals, or Little Ado about Much
- The Present Status of the Decaying Neutrino Theory
- Exploiting the Computer to Investigate Black Holes and Cosmic Censorship
- Misner Space as a Prototype for Almost Any Pathology
- Relativity and Rotation
- The First Law of Black Hole Mechanics
- Gravitational Radiation Antenna Observations
- The Back-Reaction is Never Negligible: Entropy of Black Holes and Radiation
- Toward a Thesis Topic
- Charles Misner: A Celebration of Memories
- Curriculum Vitae of C. W. Misner
- Ph. D. Theses supervised by C. W. Misner
- List of Publications of C. W. Misner
No Time Machines from Lightlike Sources in 2+1 Gravity
Published online by Cambridge University Press: 03 February 2010
- Frontmatter
- Contents
- Contributors
- Symposium Program
- Papers from both Volumes Classified by Subject
- Preface
- Charles W. Misner: Insight and Discovery
- Remarks Concerning the Geometries of Gravity and Gauge Fields
- Gravity and Unification of Fundamental Interactions
- Minisuperspaces: Symmetries and Quantization
- Quantum Cosmology
- A Pictorial History of some Gravitational Instantons
- No Time Machines from Lightlike Sources in 2+1 Gravity
- Inhomogeneity and Anisotropy Generation in FRW Cosmologies
- Misner, Kinks and Black Holes
- The Quantum Mechanics of Closed Systems
- Cosmological Vacuum Phase Transitions
- Minisuperspace as a Quantum Open System
- Ricci Flow on Minisuperspaces and the Geometry-Topology Problem
- Classical and Quantum Dynamics of Black Hole Interiors
- Matter Time in Canonical Quantum Gravity
- The Isotropy and Homogeneity of the Universe
- Recent Advances in ADM Reduction
- Some Progress in Classical Canonical Gravity
- Harmonic Map Formulation of Colliding Electrovac Plane Waves
- Geometry, the Renormalization Group and Gravity
- An Example of Indeterminacy in the Time-Development of “Already Unified Field Theory”: A Collision between Electomagnetic Plane Waves
- Non-static Metrics of Hiscock-Gott Type
- Non-Standard Phase Space Variables, Quantization and Path-Integrals, or Little Ado about Much
- The Present Status of the Decaying Neutrino Theory
- Exploiting the Computer to Investigate Black Holes and Cosmic Censorship
- Misner Space as a Prototype for Almost Any Pathology
- Relativity and Rotation
- The First Law of Black Hole Mechanics
- Gravitational Radiation Antenna Observations
- The Back-Reaction is Never Negligible: Entropy of Black Holes and Radiation
- Toward a Thesis Topic
- Charles Misner: A Celebration of Memories
- Curriculum Vitae of C. W. Misner
- Ph. D. Theses supervised by C. W. Misner
- List of Publications of C. W. Misner
Summary
Abstract
We extend the argument that spacetimes generated by two timelike particles in D=3 gravity (or equivalently by parallel-moving cosmic strings in D=4) permit closed timelike curves (CTC) only at the price of Misner identifications that correspond to unphysical boundary conditions at spatial infinity and to a tachyonic center of mass. Here we analyze geometries one or both of whose sources are lightlike. We make manifest both the presence of CTC at spatial infinity if they are present at all, and the tachyonic character of the system: As the total energy surpasses its tachyonic bound, CTC first begin to form at spatial infinity, then spread to the interior as the energy increases further. We then show that, in contrast, CTC are entirely forbidden in topologically massive gravity for geometries generated by lightlike sources.
Among the many fundamental contributions by Charlie Misner to general relativity is his study of pathologies of Einstein geometries, particularly NUT spaces, which in his words are “counterexamples to almost everything”; in particular they can possess closed timelike curves (CTC). As with other farsighted results of his which were only appreciated later, this 25-year old one finds a resonance in very recent studies of conditions under which CTC can appear in apparently physical settings, but in fact require unphysical boundary conditions engendered by identifications very similar to those he discovered. In this paper, dedicated to him on his 60th birthday, we review and extend some of this current work. We hope it brings back pleasant memories.
Introduction
Originally constructed by Gödel [1], but foreshadowed much earlier [2], spacetimes possessing CTC in general relativity came as a surprise to relativists.
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- Directions in General RelativityProceedings of the 1993 International Symposium, Maryland: Papers in Honor of Charles Misner, pp. 78 - 89Publisher: Cambridge University PressPrint publication year: 1993
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