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Astron. Astrophys. 343, 325-332 (1999)


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Pseudo-Newtonian models of a rotating black hole field

Oldich Semerák 1 and Vladimír Karas 2

1 Department of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holeovikách 2,
CZ-180 00 Praha 8, Czech Republic (e-mail: semerak@mbox.troja.mff.cuni.cz)
2 Astronomical Institute, Faculty of Mathematics and Physics, Charles University, V Holeovikách 2,
CZ-180 00 Praha 8, Czech Republic (e-mail: karas@mbox.troja.mff.cuni.cz)

Received 25 May 1998 / Accepted 20 November 1998

Abstract

A pseudo-Newtonian description of the gravitational field which yields the equations of motion resembling, as closely as possible, the geodesic equation of general relativity is found for the Kerr spacetime. The potential obtained consists of three parts, interpreted as a purely Newtonian (gravitoelectric) term, a dragging (gravitomagnetic) term, and a space-geometry correction. The accuracy of the pseudo-Newtonian model is studied by a method which compares, systematically, two large sets of trajectories: geodesics in the Kerr spacetime versus test-particle trajectories in the pseudo-Newtonian field. It is suggested that every pseudo-Newtonian model should be submitted to analogous systematic analysis before it is used in astrophysical applications. A modified Newtonian potential which accounts for the frame-dragging effects can be a practical tool in studying stationary accretion discs. Non-stationary configurations are more complicated and we will not suggest to use this approach to such topics in accretion theory as gravitomagnetic oscillations of discs and their relation to quasi-periodic sources.

Key words: accretion, accretion discs – black hole physics

Send offprint requests to: O. Semerák

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999

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