Quantization of maximally-charged slowly-moving black holes

TL;DR

This paper explores the quantization of slowly-moving extremal Reissner-Nordstrom black holes, revealing how a gauge choice resolves the issue of an ill-defined ground state by employing the DFF Hamiltonian redefinition.

Contribution

It demonstrates that the DFF Hamiltonian redefinition arises naturally from gauge fixing in black hole scattering, clarifying the role of conformal symmetry and quantization.

Findings

The original Hamiltonian lacks a ground state.

Gauge fixing introduces a well-defined Hamiltonian.

DFF redefinition corresponds to a different gauge choice.

Abstract

We discuss the quantization of a system of slowly-moving extreme Reissner-Nordstrom 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 a la 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.