Black Hole Entropy in Induced Gravity and Information Loss

The basic assumption of the induced gravity approach is that Einstein theory is an effective, low energy-form of a quantum theory of constituents. In this approach the Bekenstein-Hawking entropy S^{BH} of a black hole can be interpreted as a measure of the loss of information about constituents inside the black hole horizon. To be more exact, S^{BH} is determined by quantum correlations between "observable" and "non-observable" states with positive and negative energy $\cal E$, respectively. It is important that for non-minimally coupled constituents $\cal E$ differs from the canonical Hamiltonian $\cal H$. This explains why previous definitions of the entanglement entropy in terms of $\cal H$ failed to reproduce S^{BH}.