Excluded possibilities of geometrodynamical analog to electric charge
- W. G. Unruh
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Read on 18 May 1970 at the Gwatt Seminar on the Bearings of Topology upon Genral Relativity
Publication assisted by National Science Foundation Grant No. GP7669.
- Misner, C. W. and Wheeler, J. A. (1957). Gravitation, Electromagnetism, Unquantized Charge, and Mass as Propeerties of Curved Empty Space,Ann. Phys.,2, 525 603. Reprinted in Wheeler,Geometrodynamics, Academic Press, New York, 1961. CrossRef
- InGeometrodynamics, pp. 231, Wheeder cites H. Weyl:Raum Zeit Materie, 4th ed., Sect.34 (Berlin, 192), A. Finstein and N. Rosen (1935).Phys. Rev. 48, 73, and J. L. Synge (1947) as having previously mentioned the idea of multiply connected spaces in Genral Relativity.
- For the experimental evidence against the existence of magnetic monopoles see R. L. Fleischeret al., Phys. Rev.,177, 2029 (1969) and other references cited therein. CrossRef
- For an elementary exposition of homology theory, see for example, note 1or any textbook on homology, theory such as I. M. Singer and J. A. Thorpe,Lecture Notes on Elementary Topology and Geometry, Scott, Foreman and Company, Gleville, Illinois, 1967.
- We assume our space-time to be compact but not boundaryless. In fact for simplicity we assume throughout that our manifold is of the form [0,1]×S whereS is a boundaryless, compact, 3-dimensional manifold (a closed three-universe in physicist terminology). See R. P. Geroch,J. Math. Phys.,8, 782 (1967) for reasons for this assumption. CrossRef
- Misner, C. W. and Finklestein, D. (1959).Ann. Phys.,6, 230. CrossRef
- Wheeler, J. A., Absence of Geometrical Analog to Electric Charge, inRelativistic Fluid Mechanics and Hydrodynamics. (Ed. Wasserman and Wells).
- We note that if our tensor is already the curl of an antisymmetric tensor, the charges associated with it are all zero, and we therefore exclude these curl free tensors.
- IfT (μρ;σ)=0 thent 16 μ=(εμν∞T ρσ);μ=0.
- For an exposition of the spinor formalism see for example R. Penrose (1960).Ann. Phys.,10, 171–201 or F. Pirani's excellent lectures in the Brandeis Summer Institute Lectures on General Relativity (New Jersey, 1964) pp. 305ff. CrossRef
- Mentioned by R. Penrose (1960).Ann. Phys.,10, 183.
- Collinson, C. (1962).Proc. Camb. Phil. Soc.,58, 346. CrossRef
- C. Collinson neglects this consequence of the Bianchi identities, making some of this independent tensors dependent.
- R. Geroch has suggested a possible method of proving the nonexistence of such curl free tensors for alln for the curl free vector and 2-tensor, and investigation of his suggestion is being carried out at present.
- Excluded possibilities of geometrodynamical analog to electric charge
General Relativity and Gravitation
Volume 2, Issue 1 , pp 27-33
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- Kluwer Academic Publishers-Plenum Publishers
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- W. G. Unruh (1)
- Author Affiliations
- 1. Joseph Henry Laboratories, Princeton University, Princcton, New Jersey