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

We quantize the exterior region of a Schwarzschild–AdS black hole using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions wi, the eigenvalues of which all have multiplicity one, and spatial eigendistributions vij having the same eigenvalues but with multiplicities 1≤mi, where the mi could in principle be arbitrarily large. Regarding only the exterior region, there was no guidance how to determine the values of the mi. However, considering also the quantization of the interior region, where the same question did not arise since the mi could be chosen by maximizing the value, it seemed logical to choose the same values, too, in the exterior case. Since the eigenvalues in the interior are the same because the temporal Hamiltonian is the same in both cases, this choice defined a unitary equivalence between the respective Hilbert spaces and the respective Hamiltonians. Hence, there is no information paradox on a quantum level.