Unitarity and Holography in Gravitational Physics

          @misc{ pirsa_PIRSA:09010030,
            doi = {10.48660/09010030},
            url = {https://pirsa.org/09010030},
            author = {Marolf, Donald},
            keywords = {Quantum Gravity, Quantum Fields and Strings},
            language = {en},
            title = {Unitarity and Holography in Gravitational Physics},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {jan},
            note = {PIRSA:09010030 see, \url{https://pirsa.org}}
          }
          

Abstract

Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. Two properties follow from this purely gravitational behavior. The first, 'Boundary Unitarity,' holds under AdS-like boundary conditions. This is the statement that the algebra of boundary observables is independent of time; i.e., that the algebra of boundary observables at any one time t_1 in fact coincides with the algebra of boundary observables at any other time t_2. As a result, any information available at the boundary at time t_1 remains available at any other time t_2. The second, 'Perturbative Holography,' holds under either AdS-like or asymptotically flat boundary conditions. In the AdS context, it is the statement that the algebra of boundary observables at any time t includes all perturbative observables anywhere in the spacetime. In the asymptotically flat context, Perturbative Holography is that statement that the algebra of observables on I^+ within any neighborhood of i^0 contains all perturbative observables. Perturbative Holography holds about any classical solution with a regular past infinity; i.e., spacetimes which collapse to form classical black holes are explicitly allowed. We derive the above properties and discuss their implications for information in black hole evaporation.