Entanglement Temperature With Gauss-Bonnet Term

TL;DR

This paper calculates the entanglement temperature in higher-dimensional spacetimes incorporating Gauss-Bonnet corrections, revealing that certain topological terms do not affect the finite entanglement entropy, especially for small regions.

Contribution

It extends the computation of entanglement temperature to include Gauss-Bonnet terms within the Jacobson-Myers entropy functional across arbitrary dimensions.

Findings

Gauss-Bonnet term does not contribute to finite entanglement entropy in four dimensions.

Weyl-squared term does not affect entanglement entropy.

Calculations are valid for small entangling regions using the normal Hamiltonian.

Abstract

We compute the entanglement temperature using the first law-like of thermodynamics, $\Delta E=T_{ent} \Delta S_{EE}$, up to Gauss-Bonnet term in the Jacobson-Myers entropy functional in any arbitrary spacetime dimension. The computation is done when the entangling region is the geometry of a slab. We also show that such a Gauss-Bonnet term, which becomes a total derivative, when the co-dimension two hypersurface is four dimensional, does not contribute to the finite term in the entanglement entropy. We observe that the Weyl-squared term does not contribute to the entanglement entropy. It is important to note that the calculations are performed when the entangling region is very small and the energy is calculated using the normal Hamiltonian.