Black hole entropy in induced gravity and information loss

The basic assumption of the induced gravity approach is that Einstein theor y 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 in terpreted 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 co rrelations between "observable" and "non-observable" states with positive a nd negative energy E, respectively. It is important that for non-minimally coupled constituents E differs from the canonical Hamiltonian H. This expla ins why previous definitions of the entanglement entropy in terms of H fail ed to reproduce S-BH.