Quantization of maximally charged slowly moving black holes

We discuss the quantization of a system of slowly moving extreme Reissner-Nordström black holes. In the near-horizon limit, this system has been shown to possess an SL(2,R) conformal symmetry. However, the Hamiltonian appears to have no well-defined ground state. This problem can be circumvented by a redefinition of the Hamiltonian due to de Alfaro, Fubini, and Furlan (DFF). We apply the Faddeev-Popov quantization procedure to show that the Hamiltonian with no ground state corresponds to a gauge in which there is an obstruction at the singularities of moduli space requiring a modification of the quantization rules. The redefinition of the Hamiltonian in the manner of DFF corresponds to a different choice of gauge. The latter is a good gauge leading to standard quantization rules. Thus the DFF trick is a consequence of a standard gauge-fixing procedure in the case of black hole scattering.

DOI:10.1103/PhysRevD.63.104018