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.