BLACK-HOLES AS QUANTUM MEMBRANES

We propose a quantum description of black holes. The degrees of freedom to be quantized are identified with the microscopic degrees of freedom of the horizon, and their dynamics is governed, at an effective level, by the action of the relativistic bosonic membrane in D = 4. We find that quantum black holes are not characterized uniquely by mass, charge and angular momentum, but there is also a quasi-continuum of membrane levels. In this approach, it is possible to assign a wave-function to the horizon, derive the Schrodinger equation that it obeys and display the solution explicitly. In general, it emerges a consistent and plausible description of black holes as objects which absorb, thermalize and emit radiation in a way which is not fundamentally different from any other macroscopic object. The limits of validity of the membrane approach rum out to coincide with the known limits of validity of the thermodynamical description of black holes.