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Prog. Theor. Phys. Vol. 12 No. 1 (1954) pp. 17-30

On Static Solutions of Einstein's Generalized Theory of Gravitation, I

Mineo Ikeda

Research Institute for Theoretical Physics, Hiroshima University, Takehara-machi, Hiroshima-ken

(Received March 31, 1954)

Abstract:

In Einstein's generalized theory of gravitation, we clarify the expressions of the basic quantity of the electromagnetic field and define “field strength” so as to introduce “four-vector potential”. When the distribution of matter and charge is static and spherically symmetric, we can choose, by using the electrostatic potential, a suitable boundary condition independently of the coordinate system used and can overcome the difficulty of Wyman and others. After that the asymptotic behaviour of Wyman's solution is studied and the resulting forms are found to be satisfactory. The mutual effect of matter and charge is also discussed and the results are compared with those of general relativity for a point charge.

URL : http://ptp.ipap.jp/link?PTP/12/17/
DOI : 10.1143/PTP.12.17

[ Full Text PDF : FREE ACCESS (1135K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. A. Einstein, The meaning of relativity, Princeton (1953), Appendix II, and earlier publications.
2. A. Papapetrou, Proc. R. Irish Acad. A 52 (1948), 69.
3. E. Schödinger, Proc. R. Irish Acad. A 51 (1947), 163.
4. H. Takeno, M. Ikeda and S. Abe, Prog. Theor. Phys. 6 (1951), 837[PTP].
5. M. Wyman, Canad. J. Math. 2 (1950), 427.
6. W. B. Bonnor, Proc. R. Soc. A 209 (1951), 353; ibid. 210 (1952), 427.
7. B. Kursunoglu, Proc. Phys. Soc. A 65 (1952), 81.
8. M. Ikeda, Prog. Theor. Phys. 7 (1952), 127[PTP].
9. E. Schrödinger, Communications Dublin Inst. Advanced Studies (A) No. 6 (1951).
10. A. Einstein, Rev. Mod. Phys. 20 (1948), 35[APS].
11. H. Takeno, Prog. Theor. Phys. 10 (1953), 509[PTP].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 13 No. 3 (1955) pp. 265-275 :

   On Static Solutions of Einstein's Generalized Theory of Gravitation, II

   Mineo Ikeda

2. Progress of Theoretical Physics Vol. 15 No. 1 (1956) pp. 1-11 :

   On Boundary Conditions in the Non-Symmetric Unified Field Theory

   Mineo Ikeda

3. Progress of Theoretical Physics Vol. 18 No. 2 (1957) pp. 154-162 :

   On Einstein's Relativistic Theory of the Non-Symmetric Field

   Mineo Ikeda

4. Progress of Theoretical Physics Vol. 20 No. 3 (1958) pp. 267-276 :

   A Comparison of Plane Wave Solutions in General Relativity with Those in Non-Symmetric Theory

   Hyôitirô Takeno

5. Progress of Theoretical Physics Vol. 24 No. 6 (1960) pp. 1149-1165 :

   On Some Peculiar Role of the Cosmological Constant in the General Theory of Relativity and in the Schrödinger Theory of Non-Symmetric Field

   Hidekazu Nariai and Yoshio Ueno

6. Progress of Theoretical Physics Vol. 48 No. 5 (1972) pp. 1708-1717 :

   On a New Solution of Einstein's Unified Field Theory

   Klaus Buchner

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