Local Operators in the Eternal Black Hole

TL;DR

This work extends the discussion of interior reconstruction in AdS/CFT to the eternal black hole, showing that a broad family of time-shifted thermofield states correspond to the same geometry but are glued to the boundary differently. It demonstrates that no global, state-independent bulk–boundary map can reproduce interior EFT for all such states, and introduces gauge-invariant relational observables to probe the interior. The authors then establish that resolving these issues requires state-dependent bulk-boundary maps, providing an explicit construction valid in a chosen patch of the Hilbert space and explaining why a single operator cannot describe the interior across all microstates. The results support a perspective in which smooth horizons persist in EFT for individual states, while the interior is inherently state-dependent in quantum gravity, with implications for the firewall debate and the holographic description of spacetime.

Abstract

We show that, in the AdS/CFT correspondence, states obtained by Hamiltonian evolution of the thermofield doubled state are also dual to an eternal black hole geometry, which is glued to the boundary with a time shift generated by a large diffeomorphism. We describe gauge invariant relational observables that probe the black hole interior in these states and constrain their properties using effective field theory. By adapting recent versions of the information paradox we show that these observables are necessarily described by state-dependent bulk-boundary maps, which we construct explicitly.