Department of Physics, University of Trento,

Via sommarive 14, Povo (Trento) I-38050, ITALY

E-mail: giacomin@science.unitn.it

**Classical Liouville theory and the microscopic interpretation
of black hole entropy**

**Abstract:**

In this talk it will be shown how to compute the black hole entropy
by finding a classical central charge of the Virasoro algebra of a Liouville
theory using the Cardy formula. This will be done by performing a dimensional
reduction of the Einstein-Hilbert action with the ansatz of a spherical
symmetry and writing the metric in conformally flat form. We obtain two
coupled field equations. Using the near horizon approximation the field
equation of the conformal factor decouples becoming a Liouville equation.
This theory posses a classical central charge and a Virasoro algebra that
can be used to count the black hole microstates via Cardy formula.