Casimir Effect, Achucarro-Ortiz Black Hole and the Cosmological Constant

TL;DR

This paper investigates the Casimir effect in a two-dimensional black hole spacetime, calculating the stress tensor for a scalar field in various vacua, and shows the equilibrium depends on the cosmological constant.

Contribution

It provides a novel calculation of the stress tensor in the Achucarro-Ortiz black hole without regularization, linking Casimir equilibrium to the cosmological constant.

Findings

Stress tensor explicitly calculated in three vacua

Equilibrium configurations are influenced by the cosmological constant

Casimir force balance determines black hole boundary conditions

Abstract

We treat the two-dimensional Achucarro-Ortiz black hole (also known as (1+1) dilatonic black hole) as a Casimir-type system. The stress tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional "walls" ("Dirichlet walls") is explicitly calculated in three different vacua. Without employing known regularization techniques, the expression in each vacuum for the stress tensor is reached by using the Wald's axioms. Finally, within this asymptotically non-flat gravitational background, it is shown that the equilibrium of the configurations, obtained by setting Casimir force to zero, is controlled by the cosmological constant.