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The critical luminosity at which the outward force of radiation balances the inward force of gravity plays an important role in many astrophysical systems. We present expressions for the radiation force on particles with arbitrary cross sections and analyze the radiation field produced by radiating matter, such as a disk, ring, or stellar surface, that rotates slowly around a slowly rotating gravitating mass. We then use these results to investigate the effect on the critical flux and, where possible, the critical luminosity in general relativity.
We show that if the momentum transfer cross section is independent of both frequency and direction, the critical flux for matter orbiting slowly in the rotation equator of the gravitating mass is the same to first order as it would be if the source and mass were static. If in addition the radiation field in the absence of rotation would be spherically symmetric, the critical luminosity of the system is independent of the spectrum and angular size of the radiation source and is unaffected by rotation of the source and the mass and orbital motion of the matter to first order. If instead the momentum transfer cross section is frequency- or angle-dependent, the critical flux generally depends on the angular size and spectrum of the source and is affected by rotation of the source and the mass and orbital motion of the matter to first order.
We suggest that for a system containing a rotating gravitating mass, the critical radiation flux that is likely to be most useful as an astrophysical benchmark is the flux that causes a particle initially at rest in the locally nonrotating frame (LNRF) at a given radius to remain at that radius. Finally, we discuss the maximum possible luminosity of a star powered by steady spherically symmetric radial accretion in general relativity. This research was supported in part by NSF grant PHY 91-00283 and NASA grant NAGW 1583 at the Univeristy of Illinois and NASA grant NAGW 830 at the University of Chicago.
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