????????? ?? ??????? ??????

?? ??????? ?????? ? ????????? ?? ????? ?????? ≪???? ????????≫ ?? ??????? ???????. ????? ???? ??? ?? ?????? ?????? ??? ??????? ??? ???? ?????? ????? ???????? ?? ??? ??? ?? ?????????. ?????? ????? ????? ?????? ??????? ?? ?????? ????? ?????? ??? ??? ?? ?????????. ^[1]^[2]

?? ??????? ??????? ???? ?????? ???????? ??????? ?????? ??????? ??????? ??? ???? ???? ???????? ?? ???? ??????? ??????? (???? ?? ???? ?????? ?????). ???????? ??? ???? ??????? ????? ???? ??????? ??? ?????? ?????? ??????? ??????? ????????? ?????? ??????? (4 ??) ??? ????? ??? ?????? ????? ??????? (3 ??).

??????? ??????? [ ??? ]

???????? ?????????? ??????? ??

${d^{2}x^{\mu } \over ds^{2}}+\Gamma ^{\mu }{}_{\alpha \beta }{dx^{\alpha } \over ds}{dx^{\beta } \over ds}=0\$

??? s ?? ????? ????? ?????? (??? ???? ?????? ????? ???????)? ? $\Gamma ^{\mu }{}_{\alpha \beta }$ ?? ???? ????????? (???? ??????? ??????? ????? ??????? ?? ??????? ????? ???? ??????) ????????? ?? ???????? ????????. ?? ???? ???????? ????????? ?????: 0 ?? 1 ?? 2 ?? 3 ???????? ?????? ????? ???????? ???????? α ? β. ???? ?????? ???????? ??? ?????? ?????? ?? ??? ???????? ????? ??????? ??? ??? ??? ???????? ?????? ??????? ????? ?????? ? ????? ???? ????? ????? ?????? ??????. ?????? ?????? ?????? ??? ????? ???????? ? ?? ???? ?? ???????? ???????? ????? (?? ?? ??? ??? ?????). ???? ????????? ?? ???? ????????? ??????? ???????? ???????? ??? ?? ????? ?? ?????? ?? ??????? ?? ??????? ?????? ????? ???????? ???? ????? ????? ??????? ?????????.

??????? ??????? ??????? ???????? ?????? ????? ?????? [ ??? ]

??? ????? ????? ?????? ?????? ?????????? ???????? ??? ??????? ??????? s. ????? ?? ???? ???? ??????? ???????? ??? ?????? ?????? $t\equiv x^{0}$ (??????? ???? ??????? ??? ??????? ??? ???????). ????? ???? ?????? ?????? ??????????:

${d^{2}x^{\mu } \over dt^{2}}=-\Gamma ^{\mu }{}_{\alpha \beta }{dx^{\alpha } \over dt}{dx^{\beta } \over dt}+\Gamma ^{0}{}_{\alpha \beta }{dx^{\alpha } \over dt}{dx^{\beta } \over dt}{dx^{\mu } \over dt}\ .$

???? ?? ???? ??? ?????? ??????? ?????? ?????????? ?????? ???????? ????????? ???????? ??????? ?????? ?? ???????? ??????????. ^[3] ?? ????? ?????? ??? ????? ?? ?????? ?????? ?????????? ?? ????? ???? ?????? ????? ??????? ?????? ???????? ????? ??????? . ???? ?? ??? ????? ???????? ??????? ????? ????? ????? ???? μ ?????. ??? ???? ???? ?????? ?????? ??? ????? ???? ??? ???????? ?????????? ??? ???:

${d^{2}x^{n} \over dt^{2}}=-\Gamma ^{n}{}_{00}.$

??? ???? ?????? ???????? n ????? [1?2?3]. ???? ??? ???????? ?????? ?? ???? ?????? ???????? ?? ???? ????? ?????? ????? ??? ??? ???????? ??? ??? ?????? ???????? ??????????. ??? ???? ??????? ????? ?? ??? ???? ?? ???? ?????? ??????? ??? ??????? ??????? ?????? ?? ????????.

???? ????? [ ??? ]

???????

????? [ ??? ]

^ Weinberg, Steven. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley 1972).
^ Einstein, Albert. The Meaning of Relativity , p. 113 (Psychology Press 2003).
^ Will, Clifford. Theory and Experiment in Gravitational Physics , p. 143 (Cambridge University Press 1993).

[Weinberg-1] Weinberg, Steven. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley 1972).

[2] Einstein, Albert. The Meaning of Relativity , p. 113 (Psychology Press 2003).

[3] Will, Clifford. Theory and Experiment in Gravitational Physics , p. 143 (Cambridge University Press 1993).

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