Newtonian analogue of force and motion of a free particle in the graviational field of the C-metric. (English) Zbl 0664.70029
The Newtonian analogue of force for the C-metric has been investigated. To the first-order of approximation in the absence of acceleration of the particle generating the C-metric, one component of the force vector corresponds to the Newtonian analogue of force. In general there are relativistic correction terms due to acceleration term in the C-metric. The motion of a freely falling body has been investigated. It is found that plane orbits are not possible. Also the radial fall is not possible and in the equation of the orbit there are terms having no classical analogue. They can be interpreted as the effect of the dragging of the inertial frame produced by the rectilinear acceleration.
MSC:
| 70H40 | Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
Keywords:
Newtonian analogue of force; C-metric; first-order of approximation; absence of acceleration; relativistic correction terms; inertial frameReferences:
| [1] | Bonnor, W. B.: 1983, in B. Bertottiet al. (eds.),Contributed Papers, Vol. 1, Padova, Italy, July 4-9, 1983, p. 184. |
| [2] | Carter, B.: 1968,Comm. Math. Phys. 10, 280. |
| [3] | Ehlers, J. and Kundt, W.: 1962, in L. Witten (ed.),Gravitation: An Introduction to Current Research, Wiley, New York. |
| [4] | Ernst, F. J.: 1976a,J. Math. Phys. 17, 54. · doi:10.1063/1.522781 |
| [5] | Ernst, F. J.: 1976b,J. Math. Phys. 17, 515. · doi:10.1063/1.522935 |
| [6] | Farhoosh, H. and Zimmerman, R. L.: 1979,J. Math. Phys. 20, 2272. · doi:10.1063/1.524008 |
| [7] | Farhoosh, H. and Zimmerman, R. L.: 1980,Phys. Rev. D21, 317. |
| [8] | Godfrey, B. B.: 1971,J. Math. Phys. 12, 606. · Zbl 0213.48802 · doi:10.1063/1.1665627 |
| [9] | Godfrey, B. B.: 1972,Gen. Rel. Grav. 3, 3. · doi:10.1007/BF00755917 |
| [10] | Hughston, L. P.: 1973,Comm. Math. Phys. 32, 147. · Zbl 0257.53017 · doi:10.1007/BF01645652 |
| [11] | Kramer, D., Stephani, H., MacCallum, M. A. H., and Harlt, E.: 1980,Exact Solutions of Einstein’s Field Equations, Cambridge University Press, Cambridge. · Zbl 0449.53018 |
| [12] | Kinnersley, W. and Walker, M.: 1970,Phys. D2, 1359. |
| [13] | Levi-Civit?, T.: 1918,Atti Accad. Naz. Lincei cl. Sci. Fis. Mat. Nat. Rend. 27, 343. |
| [14] | Mehra, A. L., Vaidya, P. C., and Kushwaha, R. S.: 1969,Acta Phys. Acad. Sci. Hungaricae 26, 339. · doi:10.1007/BF03157472 |
| [15] | Narlikar, V. V. and Singh, K. P.: 1951,Proc. Nat. Int. Sci. India A17, 311. |
| [16] | Newman, E. T. and Tamburino, L.: 1961,J. Math. Phys. 2, 667. · Zbl 0100.40501 · doi:10.1063/1.1703754 |
| [17] | Plebanski, J. F. and Demianski, M.: 1976,Ann. Phys. N.Y. 98, 98. · Zbl 0334.53037 · doi:10.1016/0003-4916(76)90240-2 |
| [18] | Robinson, I. and Trautman, A.: 1962,Proc. Royal Soc. London 1265, 463. |
| [19] | Singh, K. P. and Pandey, S. N.: 1960,Proc. Nat. Inst. Sci. India A26, 694. |
| [20] | Singh, K. P. and Upadhyay, R. C.: 1972,Indian J. Phys. 46, 172. |
| [21] | Singh, T. and Yadav, R. B. S.: 1980,Indian J. Pure Appl. Math. 11, 908. |
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