Quantum Black hole--White hole entangled states

TL;DR

This paper explores the quantum deformation of Schwarzschild black holes using a quantum group approach, revealing quantized properties, entangled black hole/white hole states, and modified thermodynamic characteristics.

Contribution

It introduces a quantum deformation framework for black holes based on the $U_q(h_4)$ group, providing new insights into their quantization, entanglement, and thermodynamics.

Findings

Quantization of event horizon area and mass.

Existence of entangled black hole/white hole states.

Modified entropy including logarithmic and cubic terms.

Abstract

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.