Quantizing the Exterior Region of a Kerr-AdS Black Hole Leads to a Resolution of the Information Paradox on a Quantum Level

We quantize the exterior region of an odd-dimensional Kerr-AdS black hole, in which all rotational parameters are equal, using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions wi, whose corresponding eigenvalues all have multiplicity one and spatial eigendistributions vij corresponding to the same eigenvalues but having multiplicities mi≥1. In principle, the mi may be arbitrarily large. When only the exterior region is considered, there is no criterion for determining the values of the mi. However, when the quantization of the interior region is also considered, the same ambiguity does not arise, because the multiplicities can be chosen to be maximal. It is therefore natural to use the same values in the exterior region. Because the temporal Hamiltonian is the same in both regions, the interior and exterior eigenvalues coincide, and this choice defines a unitary equivalence between the respective Hilbert spaces and Hamiltonians. The unitary equivalence between the Hilbert spaces and their respective Hamiltonians preserves the complete quantum-statistical information carried by all normal states in the interior and exterior regions of the black hole. Hence, there is no information paradox at the quantum level.