Entanglement Entropy of Reissner–Nordstrm Black Hole and Quantum Isolated Horizon

Based on the work of Ghosh and Pereze, who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon(QIH)§ the entropy of Reissner–Nordstr¨om black hole is studied.According to the Unruh temperature, the statistical entropy of quantum fields under the background of Reissner–Nordstr¨om spacetime is calculated by means of quantum statistics. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. In Reissner–Nordstr¨om spacetime it is shown that if only the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein–Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.