ON THE UNIQUENESS OF FOCK'S HARMONIC COORDINATE SYSTEMS IN THE PRESENCE OF STATIC, SPHERICALLY SYMMETRIC SOURCES
Fock's (V. Fock, The Theory of Space Time and Gravs-tation (Pergamon Press, New York), 342(1959)) harmonic'' coordinate systems in curved space flattening out toward spatial infinity are uniquely determined but for an arbftrary inhomogeneous Lorentz transformation. lntroduction of Fock's harmonic coordinate condit1ons would provide a natural way of introducing a Lorentz subgroup of the general coordinate transformation group of Einstein's gravitatlonal theory, and of defining a Minkowski metric besides the curved-space metric. This would open the way to close relations between Einstein's gravitational theory on the one hand, and Lorentz-covariant quantum field theory on the other hand. A general proof of the correctness of Fock's claim, for universes satisfying his boundary conditions, was never given rigorously. An earlier proof of this uniqueness for the Schwarzschild field around a single gravitational singularity, is extended to the case of the static and spherically symmetric field generated in some coordinate system by an extended static and spherical distribution of energy and of stresses. The uniqueness (but for the zero point of time and for a spatial rotation) of the harmonic coordinate system, in which this field is spherical and at rest around the spatia1 origin, is guaranteed by the condition that there must be a one-to-one correspondence between the points x, y, z, t of the harmonic coordinate system and the points in physical space. (auth)
- Research Organization:
- Purdue Univ., Lafayette, Ind.
- NSA Number:
- NSA-16-011137
- OSTI ID:
- 4791924
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 125; Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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