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Information × Registration Number 0219U100032, 0118U002105 , R & D reports Title Physics of high energy particles near black holes popup.stage_title Head Zаslаvskyi Oleh B., Доктор фізико-математичних наук Registration Date 08-01-2019 Organization V.N. Karazin Kharkiv National University popup.description2  We consider the metric of a generic axially symmetric rotating stationary black hole. The general approach is developed that enables us to construct coordinate frame regular near the horizon. As explicit examples, the Kerr and Kerr–Newmann-(anti-)de Sitter metrics are considered. It is shown how the rotational versions of the Painleve–Gullstrand and Doran coordinates appear in this scheme as particular cases. For the 2+1 version of the metric the direct generalization of the Lemaitre coordinate system is obtained. It is shown that the possibility of introducing a regular frame is indirectly related to the constancy of a black hole angular velocity and the rate with which the metric coefficient responsible for the rotation of spacetime tends to it. 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. Product Description popup.authors popup.nrat_date 2020-04-02 Close