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Additional resources for Acoustic Pressure Distributions, Chiefly in Reservoirs and in Pipes

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Associated with gauge "elds there are conserved charges, which can be measured using the Gauss #ux theorem. On the other hand, all physical quantities which are not coupled to the corresponding gauge "elds, like baryon number, are not strictly conserved. As a result, they either disappear during the collapse or become unmeasurable. The proof of this conjecture was given for a number of special cases. In such a proof it is not the process of collapse that is usually considered but the result of it } a stationary black hole spacetime with certain matter "elds.

The numerical integration gives for any (Ra family of black hole solutions parameterized by (r , n) as in the "0 case. The behaviour of w, m, and is qualitatively the same as for the EYM solutions, while the dilaton is a monotone function. 43) does not vanish and is given by C" N r. 26)  where " N /2 is the surface gravity and A"4 r is the area of the event horizon.  The thermodynamics of dilaton black holes depends on value of the dilaton coupling constant [306]. For small values of there is a region in the parameter space for which the speci"c heat of the solutions is positive.

This is reminiscent of a "rst-order phase transition. There is also another region in the parameter space characterized by the echoing phenomenon and the scaling behavior for the black hole mass, which can now be arbitrarily small [88]. This is explained by the existence of another intermediate attractor in the problem. The corresponding solution to the EYM equations is time-dependent. It describes the situation when there is a constant ingoing #ux of the YM radiation which comes from in"nity, completely re#ects from the origin, and then goes back to in"nity.

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Acoustic Pressure Distributions, Chiefly in Reservoirs and in Pipes by Barus C.

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