Probing black hole entropy via entanglement

In this paper, we develop a method to extract the Bekenstein-Hawking entropy of D-dimensional black holes using the entanglement entropy of a lower-dimensional conformal field theory (CFT). This approach relies on two key observations. On the gravitational side, the near-horizon geometry of extremal black holes is AdS2, and the Bekenstein-Hawking entropy is entirely determined by this two-dimensional geometry. Moreover, the higher-dimensional spherical part of the black hole metric is absorbed into the D-dimensional Newton’s constant GN(D), which can be effectively reduced to a two-dimensional Newton’s constant GN(2). On the field theory side, the entanglement entropy of two disconnected one-dimensional conformal quantum mechanics (CQM1) can be calculated. According to the Ryu-Takayanagi (RT) prescription, this entanglement entropy computes the area of the minimal surface in the AdS2 geometry. Since the near-horizon region of the black hole and the emergent spacetime derived from the entanglement entropy share the same Penrose diagram—with both the black hole event horizon and the RT surface corresponding to specific points on this diagram—the Bekenstein-Hawking entropy can be probed via entanglement entropy when these points coincide. This result explicitly demonstrates that the entanglement across the event horizon is the fundamental origin of the Bekenstein-Hawking entropy.