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

We treat the two-dimensional projection of the (2 + 1) BTZ black hole (known as Achucarro-Ortiz black hole or 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 stability of the configuration, obtained by setting Casimir force to zero, is controlled by the cosmological constant.