Nonminimal coupling, quantum scalar field stress-energy tensor and energy conditions on global anti-de Sitter space-time

TL;DR

This paper calculates the quantum scalar field stress-energy tensor in 3D anti-de Sitter space, analyzing how boundary conditions, mass, and coupling affect energy condition compliance.

Contribution

It provides the first detailed analysis of how nonminimal coupling and boundary conditions influence quantum energy conditions in AdS space.

Findings

Energy condition compliance varies with scalar field parameters.

Boundary conditions significantly impact the stress-energy tensor.

The results reveal complex dependencies on mass and coupling.

Abstract

We compute the renormalized expectation value of the stress-energy tensor operator for a quantum scalar field propagating on three-dimensional global anti-de Sitter space-time. The scalar field has general mass and nonminimal coupling to the Ricci scalar curvature, and is subject to Dirichlet, Neumann or Robin boundary conditions at the space-time boundary. We consider both vacuum and thermal states, and explore whether the weak and null energy conditions are satisfied by the quantum stress-energy tensor. We uncover a rather complicated picture: compliance with these two energy conditions depends strongly on the mass and coupling of the scalar field to the curvature, and the boundary conditions applied.