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arXiv · 1707.02860

Number of revolutions of a particle around a black hole: Is it infinite or finite?

Yu. V. Pavlov·O. B. Zaslavskii
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Abstract

We consider a particle falling into a rotating black hole. Such a particle makes an infinite number of revolutions $n$ from the viewpoint of a remote observer who uses the Boyer-Lindquist type of coordinates. We examine the behavior of $n$ when it is measured with respect to a local reference frame that also rotates due to dragging effect of spacetime. The crucial point consists here in the observation that for a nonextremal black hole, the leading contributions to $n$ from a particle itself and the reference frame have the same form being in fact universal, so that divergences mutually cancel. As a result, the relative number of revolutions turns out to be finite. For the extremal black hole this is not so, $n$ can be infinite. Different choices of the local reference frame are considered, the results turn out to be the same qualitatively. For illustration, we discuss two explicit examples - rotation in the flat spacetime and in the Kerr metric.

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Yu. V. Pavlov, O. B. Zaslavskii. 2017-07-10. Number of revolutions of a particle around a black hole: Is it infinite or finite?. https://doi.org/10.1007/s10714-017-2333-5

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