ON THE TWO-PARTICLE GRAVITATIONAL INTERACTION ENERGY PROBLEM
https://doi.org/10.29235/1561-8323-2018-62-1-41-50
Abstract
The generally relativistic motivated explicit analytic expression describing the interacting energy of the pair of nonpoint-like non-spinning masses is found. It is shown that Gibbons’ maximum tension principle allows us to remove the co-ordinate singularities so that the energy of the gravitational two-particle interaction possesses a numerically bounded minimum. It is shown that Gibbons’ maximum force treated in a purely mechanical context possesses the explicit parametric dependence on the interacting mass ratio.
Keywords
Schwarzschild black wholes,
Maximum force,
singularities abolition,
bounded energy interaction minimum
Supporting agencies: I am grateful to V. V. Кudryashov, Е. А. Тоlkachev and А. E. Shalyt-Маrgolin for assistance in the study and useful discussions.
About the Author
Lev M. Tomilchik
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief researcher
68, Nezavisimosti Ave., 220072, Minsk
References
1. Gibbons G. W. The Maximum Tension Principle in General Relativity. Foundations of Physics, 2002, vol. 32, no. 12, pp. 1891–1901. doi.org/10.1023/a:1022370717626
2. Schiller C. General relativity and cosmology derived from principle of maximum power or force. International Journal of Theoretical Physics, 2005, vol. 44, no. 9, pp. 1629–1647. doi.org/10.1007/s10773-005-4835-2
3. Tomilchik L. M., Kudryashov V. V. Conformally-Flat Metric, Position-Dependent Mass and Cold Dark Matter. Starovoitov P. (ed.) Actual Problems of MicroWorld Physics. Proceedings International School-Seminar, Gomel, Belarus, July 28–August 8, 2003. Dubna, 2004, vol. 1, pp. 24–42.
4. Tomilchik L. M. Model of massive pulsating sphere as an exact solution of the Hamiltonian self reciprocal dynamics equations. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2017, vol. 61, no. 1, pp. 36–46 (in Russian).
5. Weinstein G. On Rotating Black Holes in Equilibrium in General Relativity. Communications on Pure and Applied Mathematics, 1990, vol. 43, no. 7, pp. 903–948. doi.org/10.1002/cpa.3160430705
6. Manko V. S. Double-Reissner-Nordstrom Solution and the interaction force between two spherical masses in general relativity. Physical Review D, 2007, vol. 76, no. 12, pp. 124032 (1–6). doi.org/10.1103/physrevd.76.124032
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