Quantum black hole-white hole entangled states

We investigate the quantum deformation of the Wheeler-DeWitt equation of a Schwarzchild black hole. Specifically, the quantum deformed black hole is a quantized model constructed from the quantum Heisenberg-Weyl U-q(h(4)) group. We show that the event horizon area and the mass are quantized, degenerate, and bounded. The degeneracy of states indicates entangled quantum black hole/white hole states. Accordingly, quantum deformation provides a new framework to examine Einstein-Rosen wormhole solutions. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Schwarzschild black hole. We find an upper bound on the mass of a black hole/white hole pair. Also, at the quantum deformation level, the entropy of the black hole contains three parts: the usual Bekenstein-Hawking entropy, the logarithmic term, and a Cube of usual black hole entropy. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

We investigated the quantum deformation of the Wheeler-DeWitt equation for a Schwarzchild black hole and discovered the quantization, degeneracy, and boundedness of the event horizon area and mass. The degeneracy of states indicates the presence of entangled quantum black hole/white hole states, providing a new framework to study Einstein-Rosen wormhole solutions.