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**Unformatted text preview: **HW#5 Phys776Spring2005 Prof. Ted Jacobson Due Thursday, April 14, before class. Room 4115, (301)405-6020 jacobson@physics.umd.edu 1. Consider a three-dimensional spherical box of circumferential radius R , that is held at temperature T (as measured by a static observer on the box). Show that: (a) A black hole inside can be in equilibrium with the box (i.e. the Hawking tem- perature measured at the box is equal to T ) only if T > 3 3 / 8 R , in which case there are two equilibrium values for the mass M ( T,R ). (b) The specific heat for the larger (smaller) M ( T,R ) is positive (negative). Hence the larger black hole is (locally, at least) in stable equilibrium. Show that its mass M always satisfies R < 3 M . 2. Consider a (three-dimensional) box containing radiation and possibly a black hole in the microcanonical ensemble with total energy E . If the box is sufficiently large, the most entropic configuration will consist of pure radiation, spread out in the box. If the box is sufficiently small, the most entropic configuration will contain a black hole...

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