We review recent progress on the information paradox. We explain why exponentially small
correlations in the radiation emitted by a black hole are sufficient to resolve the original …

Abstract The Problem of Time occurs because the 'time'of GR and of ordinary Quantum
Theory are mutually incompatible notions. This is problematic in trying to replace these two …

A bstract In ordinary gravitational theories, any local bulk operator in an entanglement
wedge is accompanied by a long-range gravitational dressing that extends to the asymptotic …

Late-time dominance of entanglement islands plays a critical role in addressing the
information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath …

A bstract We consider the problem of defining localized subsystems in gauge theory and
gravity. Such systems are associated to spacelike hypersurfaces with boundaries and …

The problem of time in quantum gravity calls for a relational solution. Using quantum
reduction maps, we establish a previously unknown equivalence between three approaches …

The unifying theme of this book is the interplay among noncommutative geometry, physics,
and number theory. The two main objects of investigation are spaces where both the …

Time has a fundamentally different character in quantum mechanics and in general relativity.
In quantum theory events unfold in a fixed order while in general relativity temporal order is …

We provide a simple and explicit construction of local bulk operators that describe the
interior of a black hole in the AdS/CFT correspondence. The existence of these operators is …

A bstract We revisit the covariant phase space formalism applied to gravitational theories
with null boundaries, utilizing the most general boundary conditions consistent with a fixed …