Replica Trick in Time-Dependent Geometries

TL;DR

This paper develops a Lorentzian replica trick framework for calculating entanglement entropy in dynamic quantum and gravitational systems, unifying approaches across cosmology and black hole physics.

Contribution

It introduces a unified Lorentzian replica path integral method applicable to time-dependent quantum fields and gravity, including quantum corrections and island saddles.

Findings

Unified Lorentzian replica framework for dynamic systems

Application to cosmological spacetimes without boundaries

Identification of island saddles in gravitational contexts

Abstract

We present a unified Lorentzian replica-path-integral framework for computing entanglement entropy in fully time-dependent quantum field theories and gravitational systems. Building on this framework, we apply the real-time replica trick to cosmological spacetimes without spatial boundaries and relate it to existing proposals that identify effective dual QFT descriptions on screen-like surfaces inside the spacetime. We also extend the Lorentzian replica construction to intrinsic gravitational subsystems, focusing on Hawking radiation and including quantum corrections in purely gravitational settings lacking time-reflection symmetry. In both contexts, island-type replica saddles arise naturally. A brief review of the QFT and holographic cases is included to establish the common structure underlying these applications.