Magnetohydrodynamic Flows in Schwarzschild Geometry
Abstract
A general theory is developed for the steady axisymmetric flow of an ideal generalrelativistic magnetohydrodynamic fluid around a Schwarzschild black hole. The theory leads to a secondorder partial differential equation  a GradShafranov 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 GradShafranov 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 1986
 DOI:
 10.1086/164617
 Bibcode:
 1986ApJ...309..455M
 Keywords:

 Black Holes (Astronomy);
 Magnetohydrodynamic Flow;
 Relativity;
 Schwarzschild Metric;
 Hydrodynamic Equations;
 Operators (Mathematics);
 Particle Motion;
 Variational Principles;
 Virial Theorem;
 Astrophysics;
 BLACK HOLES;
 HYDROMAGNETICS;
 RELATIVITY