Anisotropic Unruh temperatures

TL;DR

This paper generalizes the concept of Unruh temperature to arbitrary regions by defining local temperatures through vacuum entanglement and modular Hamiltonians, revealing direction-dependent temperatures for complex shapes.

Contribution

It introduces a universal geometric formula for local temperatures in arbitrary regions, extending the Unruh effect beyond Rindler wedges and solving a generalized eikonal equation.

Findings

Universal expression for local temperatures in free scalar and fermion fields.

Explicit formulas for wall and strip geometries.

Direction-dependent temperatures for arbitrary shapes.

Abstract

The relative entropy between very high energy localized excitations and the vacuum, where both states are reduced to a spatial region, gives place to a precise definition of a local temperature produced by vacuum entanglement across the boundary. This generalizes the Unruh temperature of the Rindler wedge to arbitrary regions. The local temperatures can be read off from the short distance leading terms in the modular Hamiltonian. For free scalar and fermion fields they have a universal geometric expression that follows by solving a particular eikonal type equation in Euclidean space. This equation generalizes to any dimension the holomorphic property that holds in two dimensions. For regions of arbitrary shapes the local temperatures at a point are direction dependent. We compute their explicit expression for the geometry of a wall or strip.