Entanglement and entropy operator for strings in pp-wave time dependent background

In this Letter new aspects of string theory propagating in a pp-wave time dependent background with a null singularity are explored. It is shown the appearance of a 2d entanglement entropy dynamically generated by the background. For asymptotically flat observers, the vacuum close to the singularity is unitarily inequivalent to the vacuum at τ=−∞ and it is shown that the 2d entanglement entropy diverges close to this point. As a consequence, the positive time region is inaccessible for observers in τ=−∞. For a stationary measure, the vacuum at finite time is seen by those observers as a thermal state and the information loss is encoded as a heat bath of string states.