Adiabatic Theory Of Motion Of Bodies In The Hartle-Thorne Spacetime
Suliyeva G.B. Boshkayev K.A. Nurbakyt G. Quevedo H. Taukenova A.S. Tlemissov A.T. Tlemissova Z. Urazalina A.
15 June 2022al-Farabi Kazakh State National University
International Journal of Mathematics and Physics
2022#13Issue 179 - 86 pp.
We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the post-Newtonian approximation where the adiabatic theory is valid. As a result, we obtain the perihelion shift formula for test particles orbiting on the equatorial plane of a rotating and deformed object. Based on the perihelion shift expression, we show that the principle of superposition is valid for the individual effects of the gravitational source mass, angular momentum and quadrupole moment. The resulting formula was applied to the inner planets of the Solar system. The outcomes are in a good agreement with observational data. It was also shown that the corrections related to the Suns angular moment and quadrupole moment have little impact on the perihelion shift. On the whole, it was demonstrated that the adiabatic theory, along with its simplicity, leads to correct results, which in the limiting cases correspond to the ones reported in the literature.
Adiabatic theory , Harmonic coordinates , Perihelion shift , Post-Newtonian approximation , The Hartle-Thorne metric
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
National Nanotechnology Laboratory of Open Type (NNLOT), Almaty, Kazakhstan
Universidad Nacional Autònoma de Mèxico, Mexico
Università di Roma “La Sapienza”, Roma, Italy
Silesian University in Opava, Opava, Czech Republic
Al-Farabi Kazakh National University
National Nanotechnology Laboratory of Open Type (NNLOT)
Universidad Nacional Autònoma de Mèxico
Università di Roma “La Sapienza”
Silesian University in Opava
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