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Title:
Magnetohydrodynamic flows in Schwarzschild geometry
Authors:
Mobarry, C. M.; Lovelace, R. V. E.
Affiliation:
AA(Cornell University, Ithaca, NY), AB(Cornell University, Ithaca, NY)
Publication:
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 309, Oct. 15, 1986, p. 455-466. (ApJ Homepage)
Publication Date:
10/1986
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
Black Holes (Astronomy), Magnetohydrodynamic Flow, Relativity, Schwarzschild Metric, Hydrodynamic Equations, Operators (Mathematics), Particle Motion, Variational Principles, Virial Theorem
DOI:
10.1086/164617
Bibliographic Code:
1986ApJ...309..455M

Abstract

A general theory is developed for the steady axisymmetric flow of an ideal general-relativistic magnetohydrodynamic fluid around a Schwarzschild black hole. The theory leads to a second-order partial differential equation - a Grad-Shafranov equation - for the magnetic flux function Psi(r, Theta). A variational principle is given which leads to the equation for Psi, and which facilitates the discussion of various limits of the Grad-Shafranov equation of interest in different astrophysical situations. A virial equation is derived from the basic equations, which is used to obtain an upper bound on the total energy in the electromagnetic field in terms of the total gravitational binding energy between the black hole and the matter outside it.

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