Null states and time evolution in a toy model of black hole dynamics

Abstract

Abstract Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states eS in a gravitational system much smaller than the number of states $$ {e}^{S_{\textrm{p}}} $$ e S p predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves N = O(eS) of the possible $$ {e}^{S_{\textrm{p}}} $$ e S p perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for N ≪ eS (in which case no quantum extremal surfaces can arise). In particular, even for small N, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension D ≪ eS. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.