Black Hole Spin and Stellar Flyby Periastron Shift

Abstract

For a scenario of a close flyby of a compact star near a spinning black hole, we provide analytical and numerical estimates for the shift of trajectory periastron due to relativistic (beyond post-Newtonian) effects. More specifically, we derived a generalized expression (not limited to quasi-circular or elliptical orbits) directly linking the periastron shift and the spin of the black hole. The expression permits the estimation of black hole spin based on astronomical tracking of locations of stars traveling along highly eccentric (parabolic and hyperbolic) trajectories in close vicinity of a black hole. We also demonstrate how stars traveling on hyperbolic or parabolic trajectories may be (temporarily) captured onto quasi-circular orbits around black holes, and we quantitatively examine conditions for such scenarios.

Dynamics of Vortex Structures: From Planets to Black Hole Accretion Disks

“…For a more detailed treatment-not included in this paper-it is necessary to consider the nuances of mathematical models for hydrodynamic flows (see, for example, Refs. [26,27]), collective plasma effects [28], relativism [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], and relativistic hydrodynamics [44].…”

“…In our model (see details in Refs. [29,30]), the spacetime metric is fully characterized by the black hole's mass parameter and "spin" (for an extensive discussion, see Refs. [31][32][33][34][35][36], and the bibliographies therein).…”

“…We use the metric signature diag(+ − −−) (see, for example, Ref. [30], and references therein). To satisfy the principle of causality for moving material objects, ds 2 > 0.…”

Hot Spots in Sgr A* Accretion Disk: Hydrodynamic Insights

“…We will use the spacetime metric entirely characterized by the black hole mass parameter and its "spin" (described in our Refs. [7,8]; for more details, see also [9][10][11][12][13][14], and bibliographies therein). We will assume that the mass of the accretion disk is negligible compared to the black hole "mass" M, probably (10 −5 ÷ 10 −4 )M ; the radiative cooling does not strongly affect the dynamics of fluid motion; and the electrons and ions are very weakly coupled by Coulomb interaction and hence ions and electrons plasmas components have different temperatures, T e T i (see Ref.…”

“…For the Minkowski tensor, we use the metric signature diag(+ − −−) (see, for example, Ref. [8], and Refs. therein).…”