Dirty black holes: Thermodynamics and horizon structure.

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, 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: kTH ≤ h̄/(4πrH) ≡ h̄/ √ 4πAH . This paper will argue that this suppression is generic. Specifically, it will be shown that