A Georgiou 2003 Class. Quantum Grav. 20 359 doi:10.1088/0264-9381/20/2/309
A Georgiou
Show affiliationsWe obtain an exact form of the virial theorem in general relativity, which is sufficiently general to be applied to charged, conducting, rotating perfect fluids in electromagnetic and gravitational fields. The case of infinite conductivity is of particular importance in astrophysics and we derive the relevant equations from the general results. We indicate how to calculate the post-Newtonian limits of various expressions and show that in the absence of both, the electric and magnetic fields, they lead to Chandrasekhar's post-Newtonian virial theorem in hydrodynamics. We also note that Chandrasekhar's (Newtonian) virial theorem in hydromagnetics may be derived from the Newtonian limit of the exact equations obtained. Some possible applications are pointed out. Finally, we use the exact form of the virial theorem to obtain, in co-moving coordinates, equilibrium conditions for bounded rotating charged dust.
04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations
95.30.Sf Relativity and gravitation
41.20.Jb Electromagnetic wave propagation; radiowave propagation
95.30.Wi Dust processes (condensation, evaporation, sputtering, mantle growth, etc.)
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
Issue 2 (21 January 2003)
Received 12 August 2002, in final form 5 November 2002
Published 3 January 2003
A Georgiou 2003 Class. Quantum Grav. 20 359
M W J Bromley and J Mitroy 2000 J. Phys. B: At. Mol. Opt. Phys. 33 L325
Jan Sikora et al 2006 Phys. Med. Biol. 51 497
D C Jain et al 1981 J. Phys. D: Appl. Phys. 14 L5
Gérard Petit and Peter Wolf 2005 Metrologia 42 S138
W.J. Hogan et al 2001 Nucl. Fusion 41 567
Ali H Nayfeh and Mohammad I Younis 2004 J. Micromech. Microeng. 14 170
A K Pearce et al 2007 Metrologia 44 S67
Stephen M Merkowitz et al 2004 Class. Quantum Grav. 21 S603
M Itoh et al 1981 J. Phys. F: Met. Phys. 11 1605