Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
Donald Marolf, Henry Maxfield
Abstract
In the 1980's, work by Coleman and by Giddings and Strominger linked the\nphysics of spacetime wormholes to `baby universes' and an ensemble of theories.\nWe revisit such ideas, using features associated with a negative cosmological\nconstant and asymptotically AdS boundaries to strengthen the results, introduce\na change in perspective, and connect with recent replica wormhole discussions\nof the Page curve. A key new feature is an emphasis on the role of null states.\nWe explore this structure in detail in simple topological models of the bulk\nthat allow us to compute the full spectrum of associated boundary theories. The\ndimension of the asymptotically AdS Hilbert space turns out to become a random\nvariable $Z$, whose value can be less than the naive number $k$ of independent\nstates in the theory. For $k>Z$, consistency arises from an exact degeneracy in\nthe inner product defined by the gravitational path integral, so that many a\npriori independent states differ only by a null state. We argue that a similar\nproperty must hold in any consistent gravitational path integral. We also\ncomment on other aspects of extrapolations to more complicated models, and on\npossible implications for the black hole information problem in the individual\nmembers of the above ensemble.