The isolated horizon framework has provided
surprising insights into the properties of hairy black holes in
equilibrium [19, 77, 75
, 26
, 21
, 76
]. While the zeroth
and first laws go through in a straightforward manner, the notion
of the horizon mass now becomes much more subtle and its properties
have interesting consequences. The framework also suggests a new
phenomenological model of colored black holes as bound states of ordinary, uncolored black
holes and solitons. This model successfully explains the
qualitative behavior of these black holes, including their
stability and instability, and provides unexpected quantitative relations between colored black
holes and their solitonic analogs.
In these theories, matter fields are minimally
coupled to gravity. If one allows non-minimal couplings, the first
law itself is modified in a striking fashion: Entropy is no longer
given by the horizon area but depends also on the matter fields.
For globally stationary space-times admitting bifurcate Killing
horizons, this result was first established by Jacobson, Kang, and
Myers [123], and by Iyer and
Wald [183
, 184
] for a general class
of theories. For scalar fields non-minimally coupled to gravity, it
has been generalized in the setting of Type II WIHs [22
]. While the
procedure does involve certain technical subtleties, the overall
strategy is identical to that summarized in Section 4.1. Therefore we will not review this
issue in detail.
This section is divided into two parts. In the first, we discuss the mechanics of weakly isolated horizons in presence of dilatons and Yang-Mills fields. In the second, we discuss three applications. This entire discussion is in the framework of isolated horizons because the effects of these fields on black hole dynamics remain largely unexplored.