  We study the system formed by a gaz of black holes and strings within a
microcanonical formulation. We derive the microcanonical content of the system:
entropy, equation of state, number of components N, temperature T and specific
heat. The pressure and the specific heat are negative reflecting the
gravitational unstability and a non-homogeneous configuration. The asymptotic
behaviour of the temperature for large masses emerges as the Hawking
temperature of the system (classical or semiclassical phase) in which the
classical black hole behaviour dominates, while for small masses (quantum black
hole or string behavior) the temperature becomes the string temperature which
emerges as the critical temperature of the system. At low masses, a phase
transition takes place showing the passage from the classical (black hole) to
quantum (string) behaviour. Within a microcanonical field theory formulation,
the propagator describing the string-particle-black hole system is derived and
from it the interacting four point scattering amplitude of the system is
obtained. For high masses it behaves asymptotically as the degeneracy of states
of the system (ie duality or crossing symmetry). The microcanonical propagator
and partition function are derived from a (Nambu-Goto) formulation of the
N-extended objects and the mass spectrum of the black-hole-string system is
obtained: for small masses (quantum behaviour) these yield the usual pure
string scattering amplitude and string-particle spectrum M_n\approx \sqrt{n};
for growing mass it pass for all the intermediate states up to the pure black
hole behaviour. The different black hole behaviours according to the different
mass ranges: classical, semiclassical and quantum or string behaviours are
present in the model.

High Energy Physics - Theory;Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology