# The Spacetime View of the Information Paradox

## TL;DR

This paper proposes a spacetime-based quantum state framework that encodes correlations across time, offering a novel resolution to the black-hole information paradox by treating time and space equally.

## Contribution

It introduces a generalized pure state defined on the entire spacetime, providing a new perspective on information preservation in black-hole evaporation.

## Key findings

- The generalized state encodes correlations between past and future.
- This approach avoids the black-hole information paradox.
- It treats time on equal footing with space in quantum states.

## Abstract

In semiclassical gravity, the final state of black-hole evaporation cannot be described by a pure state. Nevertheless, we point out that the system can be described by a generalized pure state, which is not defined on a 3-dimensional hypersurface but on the 4-dimensional spacetime describing the whole Universe at all times. Unlike the conventional quantum state, such a generalized state treats time on an equal footing with space, which makes it well suited for systems that are both quantum and relativistic. In particular, such a generalized state contains a novel type of information encoded in the correlations between future and past, which avoids the black-hole information paradox.