By Evans G. C.
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Extra info for Potentials of General Masses in Single and Double Layers. The Relative Boundary Value Problems
Sample text
The Schwarz8child Black Hole. Now we consider two simplified models: 1. The two-dimensional analogue of the gravitational collapse. Here the metric is chosen to correspond to a spherically symmetric ball of matter imploding across its event horizon in an arbitrary way; 2. The four-dimensional case ignoring the effects of backscattering. (137). 138) 29 where T = 21l"~B ' K, = 4~ , (surfacegravity). 139) This appears Planck spectrum. If we consider backscattering, the spectrum is not precisely Planckian, but can be regarded as "thermal" in the following sense: the black hole is in thermal equilibrium with the surrounding heat bath.
14) 36 This equation accounts properly for the relativistic flow, Doppler and gravitational redshifts, photon recapture by the black hole, and so on. The corresponding spectrum is hv lOMe V. 15) I'V Thus, the emission consists largely of very hard X -rays and 'Y -rays. But comparing Eq. (13), Eq. (14) reveals a very low efficiency (to) for the conversion of rest-mass energy into radiation: to = L[! M I'V 6 x 10- 11 (~) (~)-3/2 (~). 16) 104 The presence of tangled magnetic fields, leading to synchrotron radiation in addition to bremsstrahlung, can increase the efficiency.
MEMBRANE PARADIGM (Thorne, Price and Macdonald, 1986) Basic Idea. We can think of each layer of black hole atmosphere as acquiring, when it sinks through the stretched horizon, the contemporary values of the stretched horizon's mass, angular momentum, angular velocity, surface gravity, surface temperature, and entropy. Each layer then retains those values forever as it sinks at the local speed of light toward the true horizon. Correspondingly, at a universal time we can regard the above quantities as functions of height in the hole's atmosphere.
Potentials of General Masses in Single and Double Layers. The Relative Boundary Value Problems by Evans G. C.
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