Exact Mathisson−Papapetrou Equations in the Schwarzschild Metric with Integrals of Motion
DOI:
https://doi.org/10.15407/ujpe56.9.869Keywords:
-Abstract
A new representation for exact Mathisson–Papapetrou equations under the Mathisson–Pirani condition in the Schwarzschild gravitational field, which does not contain third-order derivatives with respect to spinning-particle coordinates, has been obtained. For this purpose, the integrals of energy and angular momentum of a spinning particle, as well as a differential relation following from the Mathisson–Papapetrou equations for an arbitrary metric, are used. The form of the equations obtained is adapted for their computer integration and further researches dealing with the influence of the spin-curvature interaction on particle's behavior in the gravitational field imposing no restrictions on the particle's velocity and spin orientation.
References
M. Mathisson, Acta Phys. Polon. 6, 163 (1937).
A. Papapetrou, Proc. R. Soc. A 209, 248 (1951).
https://doi.org/10.1098/rspa.1951.0200
W.G. Dixon, Proc. R. Soc. A 314, 499 (1970)
https://doi.org/10.1098/rspa.1970.0020
Philos. Trans. A 217, 59 (1974)
https://doi.org/10.1016/0042-6822(74)90217-7
Acta Phys. Polon. B Proc. Suppl. 1, 27 (2008).
C. Möller, Commun. Dublin Inst. Adv. Stud Ser. A 5, 3 (1949).
B. Mashhoon, J. Math. Phys. 12, 1075 (1971).
https://doi.org/10.1063/1.1665699
M. Mathisson, Acta Phys. Polon. 6, 218 (1937).
J. Weyssenhoff and A. Raabe, Acta Phys. Polon. 9, 7 (1947).
W. Tulczyjew, Acta Phys. Polon. 18, 393 (1959);
F. Pirani, Acta Phys. Polon. 15, 389 (1956).
https://doi.org/10.1016/0003-2670(56)80072-X
B.M. Barker and R.F. O'Connell, Gen. Relat. Gravit. 11, 149 (1979).
https://doi.org/10.1007/BF00756587
A.N. Aleksandrov, Kinem. Fiz. Nebesn. Tel 7, 13 (1991).
R.M. Plyatsko and O.B. Stefanyshyn, Zh. Fiz. Dosl. 13, 3 (2009).
https://doi.org/10.30970/jps.13.3003
R. Plyatsko, O. Stefanyshyn, and M. Fenyk, Phys. Rev. D 82, 044015 (2010).
https://doi.org/10.1103/PhysRevD.82.044015
R.M. Plyatsko, Manifestations of Gravitational Ultra-Relativistic Spin-Orbit Interaction (Naukova Dumka, Kyiv, 1988) (in Ukrainian).
B. Mashhoon, Ann. Phys. 89, 254 (1975)
https://doi.org/10.1016/0003-4916(75)90304-8
D. Bini, C. Cherubini, A. Geralico, and R.T. Jantzen, Int. J. Mod. Phys. 15, 737 (2006).
https://doi.org/10.1142/S0218271806008498
E. Corinaldesi and A. Papapetrou, Proc. R. Soc. A 209, 258 (1951).
R. Micoulaut, Z. Phys. 206, 394 (1967).
https://doi.org/10.1007/BF01326498
R. Wald, Phys. Rev. D 6, 406 (1972).
https://doi.org/10.1103/PhysRevD.6.406
S. Rasband, Phys. Rev. Lett. 30, 111 (1973).
https://doi.org/10.1103/PhysRevLett.30.111
K.P. Tod, F. de Felice, and M. Calvani, Nuovo Cim. B 34, 365 (1976).
https://doi.org/10.1007/BF02728614
M. Carmeli, Ch. Charach, and M. Kaye, Phys. Rev. D 15, 1501 (1977).
https://doi.org/10.1103/PhysRevD.15.1501
M.A. Abramowicz and M. Calvani, Mon. Not. R. Astron. Soc. 189, 621 (1979).
https://doi.org/10.1093/mnras/189.3.621
K. Svirskas, K. Pyragas, and A. Lozdiene, Astrophys. Space Sci. 149, 39 (1988).
https://doi.org/10.1007/BF00640464
R.H. Rietdijk and J.W. van Holten, Class. Quant. Gravit. 10, 575 (1993).
https://doi.org/10.1088/0264-9381/10/3/017
S. Suzuki and K. Maeda, Phys. Rev. D 55, 4848 (1997).
https://doi.org/10.1103/PhysRevD.55.4848
S. Suzuki and K. Maeda, Phys. Rev. D 58, 023005 (1998).
https://doi.org/10.1103/PhysRevD.58.023005
O. Semerak, Mon. Not. R. Astron. Soc. 308, 863 (1999).
https://doi.org/10.1046/j.1365-8711.1999.02754.x
O.S. Ivanitskaya, Lorentz Basis and Gravitational Effects in Einstein's Theory of Gravitation (Nauka i Tekhnika, Minsk, 1979) (in Russian).
A.P. Ryabushko, Motion of Bodies in the General Theory of Relativity (Vysheishaya Shkola, Minsk, 1972) (in Russian).
A.M. Hossain and A. Mainuddin, Ann. Phys. (NY) 282, 157 (2000).
M. Hartl, Phys. Rev. D 67, 024005 (2003)
https://doi.org/10.1103/PhysRevD.67.024005
Phys. Rev. D 67, 104023 (2003).
A.M. Hossain, Gen. Relat. Gravit. 35, 285 (2003).
D. Bini, F. de Felice, and A. Geralico, Class. Quant. Gravit. 21, 5427 (2004).
https://doi.org/10.1088/0264-9381/21/23/009
D. Bini, F. de Felice, and A. Geralico, Class. Quant. Gravit. 21, 5441 (2004).
https://doi.org/10.1088/0264-9381/21/23/010
S.B. Faruque, Phys. Lett. A 327, 95 (2004).
https://doi.org/10.1016/j.physleta.2004.05.018
L.M. Burko, Phys. Rev. D 69, 044011 (2004).
https://doi.org/10.1103/PhysRevD.69.044011
C. Chicone, B. Mashhoon, and B. Punsly, Phys. Lett. A 343, 1 (2005).
https://doi.org/10.1016/j.physleta.2005.05.072
D. Bini, A. Geralico, and F. de Felice, Int. J. Mod. Phys. D 14, 1793 (2005).
https://doi.org/10.1142/S0218271805007358
D. Bini, F. de Felice, A. Geralico, and R.T. Jantzen, Class. Quant. Gravit. 22, 2947 (2005).
https://doi.org/10.1088/0264-9381/22/14/007
R. Plyatsko, Class. Quant. Gravit. 22, 1545 (2005).
https://doi.org/10.1088/0264-9381/22/9/004
B. Mashhoon and D. Singh, Phys. Rev. D 74, 124006 (2006).
https://doi.org/10.1103/PhysRevD.74.124006
D. Bini, F. de Felice, A. Geralico, and R.T. Jantzen, Class. Quant. Gravit. 23, 3287 (2006).
https://doi.org/10.1088/0264-9381/23/10/003
D. Singh, Phys. Rev. D 78, 104028 (2008).
https://doi.org/10.1103/PhysRevD.78.104029
M. Mortazavimanesh and M. Mohseni, Gen. Relat. Gravit. 41, 2697 (2009).
https://doi.org/10.1007/s10714-009-0798-6
M. Mohseni, Gen. Relat. Gravit. 42, 2477 (2010).
https://doi.org/10.1007/s10714-010-0995-3
Yu. Obukhov and D. Puetzfeld, Phys. Rev. D 83, 044024 (2011).
https://doi.org/10.1103/PhysRevD.83.044024
Ya.M. Yakupov, Aspirant. Raboty Fiz. Kazan. Univ. 13, 254 (1975).
L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1983).
S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, Oxford, 1983).
https://doi.org/10.1007/978-94-009-6469-3_2
S. Wong, Int. J. Theor. Phys. 5, 221 (1972)
https://doi.org/10.1007/BF00670477
L. Kannenberg, Ann. Phys. (NY) 103, 64 (1977)
https://doi.org/10.1016/0003-4916(77)90260-3
J. Audretsch, J. Phys. A 14, 411 (1981)
https://doi.org/10.1016/0031-3203(81)90086-8
A. Gorbatsievich, Acta Phys. Polon. B 17, 111 (1986)
A. Barut and M. Pavsic, Class. Quant. Gravit. 4, 41 (1987)
https://doi.org/10.1088/0264-9381/4/3/002
F. Cianfrani and G. Montani, Europhys. Lett. 84, 30008 (2008)
https://doi.org/10.1209/0295-5075/84/30008
Int. J. Mod. Phys. A 23, 1274 (2008)
https://doi.org/10.1142/S0217751X08040214
Yu. Obukhov, A. Silenko, and O. Teryaev, Phys. Rev. D 80, 064044 (2009).
https://doi.org/10.1103/PhysRevD.80.064044
R. Plyatsko and O. Stefanyshyn, Acta Phys. Polon. B 39, 23 (2008).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
