Local Operators in the Eternal Black Hole

TL;DR

This paper explores how certain evolved states in AdS/CFT correspond to eternal black holes with shifted boundaries, using gauge-invariant observables and state-dependent mappings to probe the black hole interior.

Contribution

It demonstrates that Hamiltonian-evolved thermofield double states are dual to shifted eternal black holes and constructs explicit state-dependent bulk-boundary maps for interior probing.

Findings

States are dual to black holes with boundary time shifts

Gauge-invariant observables probe the black hole interior

Explicit state-dependent bulk-boundary maps are constructed

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.