New conservation laws in general-relativistic magnetohydrodynamics

Journal Article · Fri Sep 15 04:00:00 EDT 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.18.1809· OSTI ID:6677120

Bekenstein, J D; Oron, E

The flow of magnetized plasma is governed by a large number of coupled equations (Maxwell's, Euler's, conservation of energy and of baryon number) so that the solution of a problem in general-relativistic magnetohydrogynamics is very complicated, even if symmetries are present. We present here a number of new conservation laws which make the solution process easier. We obtain the general criteria for a flux conservation law to exist. We apply them to obtain the relativistic versions of the conservation of magnetic flux and of Kelvin's circulation theorem for an unmagnetized fluid, as well as a new flux conservation law for a charged fluid. For stationary and axial symmetry we find conservation laws for each component of the Maxwell tensor; these are valid even if the plasma is nonperfect. For perfect plasma we find magnetic generalizations of the relativistic Bernoulli theorems for an unmagnetized fluid. We also find a new conservation law without previous analog. As an application of our results we show that extraction of rotational energy from a black hole by interaction with a magnetized plasma is not possible in the stationary state. This contradicts previous conclusions based on the approximation of geodesic flow. Finally, still for stationary and axial symmetry, we find the magnetic generalization of Kelvin's circulation theorem. With its help we reduce the problem of solving for the field of flow and for the magnetic field to the solution of two equations: baryon conservation and a Hamilton-Jacobi-type equation. A by-product of our derivations is an explicit formula for the strength of the magnetic field in terms of fluid variables.

• Research Organization: Department of Physics, Ben Gurion University of the Negev, Beer-Sheva, 84120 Israel
• OSTI ID: 6677120
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 18:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640430 -- Fluid Physics-- Magnetohydrodynamics
657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BLACK HOLES
BOUNDARY CONDITIONS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
ENERGY-MOMENTUM TENSOR
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FLUID MECHANICS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HYDRODYNAMICS
MAGNETOHYDRODYNAMICS
MECHANICS
NEUTRON STARS
PLASMA
STARS
TENSORS