  In this article we compute the black hole entropy by finding a classical
central charge of the Virasoro algebra of a Liouville theory using the Cardy
formula. This is done by performing a dimensional reduction of the Einstein
Hilbert action with the ansatz of spherical symmetry and writing the metric in
conformally flat form. We obtain two coupled field equations. Using the near
horizon approximation the field equation for the conformal factor decouples.
The one concerning the conformal factor is a Liouville equation, it posses the
symmetry induced by a Virasoro algebra. We argue that it describes the
microstates of the black hole, namely the generators of this symmetry do not
change the thermodynamical properties of the black hole.
