Duality of Ryu-Takayanagi surfaces inside and outside the horizon

TL;DR

This paper explores how Ryu-Takayanagi surfaces in static spacetimes with horizons can be analytically continued to probe black hole interiors, demonstrating that interior areas can be reconstructed from exterior contributions, supporting black hole complementarity.

Contribution

It introduces a method to analytically continue RT surfaces into black hole horizons and reconstruct interior areas from exterior data, advancing understanding of holographic entanglement.

Findings

Interior RT surface areas can be reconstructed from exterior contributions.

Analytical continuation of RT surfaces extends into the black hole interior.

Supports the concept of black hole complementarity at the classical level.

Abstract

We study the Ryu-Takayanagi (RT) surfaces associated with timelike subregions in static spacetimes with a horizon. It is possible to find the analytical continuation of the RT surfaces that can extend into the horizon, allowing us to probe the interior of the black hole. The horizon typically divides the RT surface into two distinct parts. We demonstrate that the area of the surface inside the horizon can be reconstructed from the contributions of the surfaces outside the horizon, along with additional RT surfaces for spacelike subregions that are causally related to the timelike subregions. This result provides a concrete realization of black hole complementarity at the level of classical metric, where the spacetime in the black hole interior can be reconstructed from the degrees of freedom outside the horizon.