Magnetic extraction of black hole rotational energy: Method and results of general relativistic magnetohydrodynamic simulations in Kerr space-time

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 67, Issue 10, 2003, Pages

  Koide, Shinji ^a  

^a UNIVERSITY OF TOYAMA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COSMOS; ELEMENTARY PARTICLE; ENERGY; HYDRODYNAMICS; MAGNETIC FIELD; MAGNETISM; MATHEMATICAL MODEL; QUANTUM MECHANICS; ROTATION; SIMULATION; SPACE; TECHNIQUE;

EID: 1342304513     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.67.104010     Document Type: Article

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34. Shorthand notation used is as follows: (Formula presented) (Formula presented)
35. Here we briefly summarize one particle motion around a Kerr black hole in the equatorial plane. Equations (A21) and (A22) give (Formula presented) where the equal in the inequality corresponds to (Formula presented) The function (Formula presented) is the effective gravitational potential. A circular orbit for a particle occurs when (Formula presented) This condition gives the orbital velocity of the particle, i.e. the Kepler velocity, (Formula presented) where the positive sign corresponds to orbits that corotate with the black hole and the negative sign to counter-rotating orbits. The velocity in the FIDO frame is given by (Formula presented) In the Schwarzschild black hole case (Formula presented) the Kepler velocity is simply (Formula presented) The particle orbit is unstable when (Formula presented) and (Formula presented) or (Formula presented) where (Formula presented) is the angular momentum of the particle in the circular orbit, (Formula presented) The “last stable orbit” is determined by (Formula presented) For a Schwarzschild black hole the radius of the last stable orbit is (Formula presented) For a maximally-rotating Kerr black hole (Formula presented) the radius of the corotating particle orbit is (Formula presented) and counter-rotating orbit is (Formula presented)
36. Note: the velocity of the MHD fast mode is given by (Formula presented) where (Formula presented) is the relativistic enthalpy density.