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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
Relativity and Rotation
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
Introduction
It was an honour to be a student of Charles Misner. And it was a pleasure to work with him. It is once again an honour and a pleasure to write an article in celebration of his sixtieth birthday.
The phenomenon of rotation generates interesting physical effects and involves intriguing basic concepts. One of the earliest classic examples of this is Newton's water-pail experiment. Within the framework of the general theory of relativity rotation displays rather unusual features. These are incorporated, for instance, in the spacetime structure such as that of a rotating black hole. Dragging of inertial frames and the occurrence of the ergosphere, to name two examples, are the outcome of the rotation built into the spacetime. Rotational effects also show up in the characteristics of particle motion and associated phenomena like gyroscope precession. These effects are revealed in an elegant manner by the invariant geometrical description of particle trajectories following the directions of spacetime symmetries, assuming that the spacetime under consideration admits such symmetries. In three dimensions, this geometrical characterization involves the specification of the curvature κ and torsion τ of the curve as functions of some parameter that varies along the curve, normally the arc-length. This can be extended to higher dimensions including time and the relevant geometrical parameters would then be κ, τ1, τ2…τn-1 for n-dimensions. These parameters fit naturally into the Frenet-Serret formalism that is well known to the geometers. When the formalism is applied to timelike integral curves of space symmetries many interesting features emerge. In the major part of this article we shall briefly review the results that have been obtained in this area of investigation.
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- Directions in General RelativityProceedings of the 1993 International Symposium, Maryland: Papers in Honor of Charles Misner, pp. 347 - 357Publisher: Cambridge University PressPrint publication year: 1993