Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-03-20
Phys.Rev.D46:2445-2451,1992
Physics
High Energy Physics
High Energy Physics - Theory
[minor revisions] 22 pages, RevTeX
Scientific paper
10.1103/PhysRevD.46.2445
Considerable interest has recently been expressed in (static spherically symmetric) blackholes in interaction with various classical matter fields (such as electromagnetic fields, dilaton fields, axion fields, Abelian Higgs fields, non--Abelian gauge fields, {\sl etc}). A common feature of these investigations that has not previously been remarked upon is that the Hawking temperature of such systems appears to be suppressed relative to that of a vacuum blackhole of equal horizon area. That is: $k T_H \leq \hbar/(4\pi r_H) \equiv \hbar/\sqrt{4\pi A_H}$. This paper will argue that this suppression is generic. Specifically, it will be shown that \[ k T_H = {\hbar\over4\pi r_H} \; e^{-\phi(r_H)} \; \left( 1 - 8\pi G \; \rho_H \; r_H^2 \right). \] Here $\phi(r_H)$ is an integral quantity, depending on the distribution of matter, that is guaranteed to be positive if the Weak Energy Condition is satisfied. Several examples of this behaviour will be discussed. Generalizations of this behaviour to non--symmetric non--static blackholes are conjectured.
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