AG Mathematische Physik, Albert Much (Uni Leipzig): Semiclassical Einstein Equations from QFT via modular theory

Albert Much (Uni Leipzig)

Semiclassical Einstein Equations from QFT via modular theory

Abstract: Jacobson showed that the Einstein equations follow from the
thermodynamic relation δQ = T δS, where Q is the heat flux, T the
temperature and S the entropy, applied to local Rindler horizons, using
quantum field theoretic input such as the Unruh effect. This raises the
question of whether gravity can be derived entirely within quantum field
theory (QFT).

In this talk, I present a QFT-based extension of Jacobson’s argument
formulated in terms of relative entropy, a well-defined and finite
entropic quantity for local algebras in QFT. Approximating small
spacetime regions by Minkowski space, we compute the relative entropy
between the vacuum and coherent excitations of a Klein-Gordon field on a
local Rindler horizon using modular theory. The resulting expression is
governed by the stress-energy tensor and encodes the energy flux across
the horizon. Identifying the variation of relative entropy with the area
variation of the horizon then reproduces the semiclassical Einstein
equations, providing a quantum-information-theoretic perspective on
gravitational dynamics.

This talk is based on joint work with Philipp Dorau (published in Phys.
Rev. Lett. 136, 091602 (2026), https://arxiv.org/abs/2510.24491).