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Positivity of Entropy in the SemiClassical Theory of Black Holes and Radiation  David Hochberg
; Thomas Kephart
; James W. York
;  Date: 
22 Mar 1993  Journal:  Phys.Rev. D48 (1993) 479484  Abstract:  Quantum stressenergy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {it all} regular renormalized stressenergy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $Delta S$ has a local minimum there. Explicit calculation shows that indeed $Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stressenergy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the backreaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The backreaction, no matter how "small",  Source:  arXiv, grqc/9211009  Services:  Forum  Review  PDF  Favorites 


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