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Rotating Disc around a Schwarzschild Black Hole

Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, CZ-180 00 Prague, Czech Republic
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Universe 2020, 6(2), 27; https://doi.org/10.3390/universe6020027
Received: 14 December 2019 / Revised: 22 January 2020 / Accepted: 26 January 2020 / Published: 3 February 2020
(This article belongs to the Special Issue Rotation Effects in Relativity)
Metric for a linear perturbation of Schwarzschild due to a rotating thin disc.
A stationary and axisymmetric (in fact circular) metric is reviewed which describes the first-order perturbation of a Schwarzschild black-hole space-time due to a rotating finite thin disc encircling the hole symmetrically. The key Green functions of the problem (corresponding to an infinitesimally thin ring)—the one for the gravitational potential and the one for the dragging angular velocity—were already derived, in terms of infinite series, by Will in 1974, but we have now put them into closed forms using elliptic integrals. Such forms are more practical for numerical evaluation and for integration in problems involving extended sources. This last point mostly remains difficult, but we illustrate that it may be workable by using the simple case of a finite thin disc with constant Newtonian surface density. View Full-Text
Keywords: gravitation; relativity; black-hole physics; dragging gravitation; relativity; black-hole physics; dragging
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MDPI and ACS Style

Semerák, O.; Čížek, P. Rotating Disc around a Schwarzschild Black Hole. Universe 2020, 6, 27. https://doi.org/10.3390/universe6020027

AMA Style

Semerák O, Čížek P. Rotating Disc around a Schwarzschild Black Hole. Universe. 2020; 6(2):27. https://doi.org/10.3390/universe6020027

Chicago/Turabian Style

Semerák, Oldřich; Čížek, Pavel. 2020. "Rotating Disc around a Schwarzschild Black Hole" Universe 6, no. 2: 27. https://doi.org/10.3390/universe6020027

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