By Einstein A.
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Rotating black holes, as defined by means of the Kerr space-time, are the foremost to figuring out the main violent and lively phenomena within the Universe, from the center cave in of huge supernova explosions generating robust bursts of gamma rays, to supermassive black gap engines that energy quasars and different energetic galactic nuclei.
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In the hands of Boltzmann and Gibbs this approach was outstandingly successful. The problem of counting states gains great clarity if one adopts a quantum-mechanical viewpoint. According to quantum mechanics the microstates do not form a continuum but a discrete set. There is an integral number of such states; they can be counted. Thus each spectral line of an atom corresponds to the emission of light quanta (photons) of definite energy, the atoms at the same time making transitions between two sharply defined discrete states, each of definite energy.
As a result of this postulate, the probability that the system is in the macrostate specified by (E, V, N, α) is proportional to Ω(E, V, N, α). The equilibrium state of the system corresponds to a particular value of α. We now make a second postulate: equilibrium corresponds to that value of α for which Ω(E, V, N, a) attains its maximum value, with (E, V, N) fixed. The meaning of this equilibrium postulate is thus that the equilibrium state is the state of maximum probability: it corresponds to the maximum statistical weight.
F. 23) in the circuit. 24) The system here consists of the solenoid and the specimen. In Fig. 13 the system is marked off by the dashed lines. When compressing a gas (Fig. 7) the analogously defined system — on which the external agency does work — consists of cylinder, piston and gas. We rewrite Eq. 24) by substituting for i and from Eqs. 25) where V = AL. 21) and is the magnetization (magnetic moment per unit volume) of the specimen. Eq. 28) Pippard has shown that Eq. 28) also holds if the fields depend on position.