  We discuss the most general effective Lagrangian obtained from the assumption
that the degrees of freedom to be quantized, in a black hole, are on the
horizon. The effective Lagrangian depends only on the induced metric and the
extrinsic curvature of the (fluctuating) horizon, and the possible operators
can be arranged in an expansion in powers of $\mpl/M$, where $\mpl$ is the
Planck mass and $M$ the black hole mass. We perform a semiclassical expansion
of the action with a formalism which preserves general covariance explicitly.
Quantum fluctuations over the classical solutions are described by a single
scalar field living in the 2+1 dimensional world-volume swept by the horizon,
with a given coupling to the background geometry. We discuss the resulting
field theory and we compute the black hole entropy with our formalism.
