Adiabatic theory in Kerr spacetimes
Boshkayev K. Nurbakyt G. Quevedo H. Suliyeva G. Tlemissov A. Tlemissova Z. Dalelkhankyzy A. Taukenova A. Urazalina A. Stuchlík Z. Beissen N. Gumarova S.
May 2024Springer
General Relativity and Gravitation
2024#56Issue 5
We outline the essential features of the adiabatic theory and demonstrate how test particle motion in general relativity may be investigated using it. The theory relies on adiabatic invariants and vector elements of the orbits. We derive a specific representation of the Kerr metric in harmonic coordinates, which enables us to obtain a general formula for the perihelion shift of test particles orbiting on the non-equatorial plane of a rotating central object. This proves the applicability of the adiabatic theory in Einstein’s gravity. We demonstrate that, for the individual effects of the gravitational source mass and angular momentum up to the second order, the principle of superposition is satisfied. We show that, in addition to its simplicity, the adiabatic theory produces correct results that, in the limiting cases, correspond to the ones reported in the literature.
Adiabatic theory , Harmonic coordinates , Kerr metric , Perihelion shift , Post-Newtonian approximation
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Al-Farabi Kazakh National University, Al-Farabi, 71, Almaty, 050040, Kazakhstan
Institute of Nuclear Physics, Ibragimova, 1, Almaty, 050032, Kazakhstan
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico city, Mexico
Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”, Roma, Italy
Fesenkov Astrophysical Institute, Observatory, 23, Almaty, 050020, Kazakhstan
Institute of Physics, Silesian University in Opava, Bezrucovo nam. 13, Opava, CZ-74601, Czech Republic
Kazakh National Women’s Teacher Training University, Ayteke Bi, 99, Almaty, 050000, Kazakhstan
Al-Farabi Kazakh National University
Institute of Nuclear Physics
Instituto de Ciencias Nucleares
Dipartimento di Fisica and ICRA
Fesenkov Astrophysical Institute
Institute of Physics
Kazakh National Women’s Teacher Training University
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