Thorne, Kip S. (1965) Energy of infinitely long, cylindrically symmetric systems in general relativity. Physical Review, 138 (1B). B251B266. ISSN 0031899X. http://resolver.caltech.edu/CaltechAUTHORS:THOpr65b

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Abstract
A definition of energy is proposed for systems invariant under rotations about, and translations along, a symmetry axis. This energy (which is called "cylindrical energy" or "C energy") takes the form of a covariant vector Pi, which obeys the conservation law Pi; i=0. C energy is localizable and locally measurable: The component of Pi along the world line of an observer is the Cenergy density he measures. Near the symmetry axis of a static system, where strong gravitational fields are absent, Cenergy density reduces to proper mass density T00. C energy is propagated by EinsteinRosen gravitational waves and by cylindrical electromagnetic waves. In vacuo and in the presence of electromagnetic fields the C energy on a spacelike hypersurface is minimized when the system is static; and the difference between the "potential" part and the "kinetic" part is a Lagrangian for the EinsteinMaxwell field equations. C energy can be a powerful tool in the analysis of finite as well as infinite cylindrically symmetric systems. Here it is used to elucidate the nature of EinsteinRosen gravitational radiation, and to suggest and support the conjecture of flux resistance to gravitational collapse: In any configuration of electromagnetic fields collapsing toward a singularity, each electric and magneticfield line is either entirely ejected from the collapsing region or entirely swallowed by it as collapse proceeds; there can be no flux threading a collapsed region.
Item Type:  Article 

Additional Information:  ©1965 The American Physical Society. Received 30 September 1964; revised 7 December 1964. The author is indebted to Professor J. A. Wheeler for many discussions in which he emphasized the role that an energylike quantity could play in the stability analysis of Melvin’s magnetic universe. It was out of these discussions that the work presented here grew. Professor Wheeler and Professor M. A. Melvin both provided valuable criticism of this presentation of C energy. 
Group:  TAPIR 
Issue or Number:  1B 
Record Number:  CaltechAUTHORS:THOpr65b 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:THOpr65b 
Alternative URL:  http://dx.doi.org/10.1103/PhysRev.138.B251 
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ID Code:  3212 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  22 May 2006 
Last Modified:  26 Dec 2012 08:53 
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