  We consider a spherically symmetric black hole in equilibrium with
surrounding classical matter that is characterized by a nonlinear dependence of
the radial pressure p_{r} on the density {\rho}. We examine under which
requirements such an equilibrium is possible. It is shown that if the radial
and transverse pressures are equal (Pascal perfect fluid), equation of state
should be approximately linear near the horizon. The corresponding restriction
on ((dp_{r})/(d{\rho})) is a direct generalization of the result, previously
found for an exactly linear equation of state. In the anisotropic case there is
no restriction on equation of state but the horizon should be simple
(nondegenerate).

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics