The frozen vacuum problem and operator algebras

Black hole information paradox is a fundamental problem in our understanding of black holes in quantum gravity. This issue has been re-emphasised by what is called the firewall paradox, an inconsistency between widely held assumptions about unitary black hole evaporation and validity of effective field theory in the gravitational field of a black hole. Proposed resolutions for this paradox have led to even more serious problems such as violation of the Born rule, and thus a modification of standard quantum mechanics; or the frozen vacuum problem. On the other hand, recently there has been a renewed interest in understanding the operator algebraic properties of semiclassical gravity. In this talk, I will review the above problems and discuss how they can be phrased in the operator algebraic setting.