Casimir effect, Achucarro-Ortiz black hole, and the cosmological constant

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.

The energy-momentum tensor in the 1 + 1 dimensional non-rotating BTZ black hole

“…A similar study of the energy-momentum tensor in the BTZ black hole in 1+1 dimensions with walls has been done in[6]. The results of this work can be considered complementary to the present work.…”

Casimir Effect for the Massless Dirac Field in Two-Dimensional Reissner–nordström Space–time

“…From Refs. [15,[10][11][12], we know that, in the lower-dimensional case, if the energy-momentum tensor of a certain field confined by an exterior boundary in the Minkowski spacetime can be obtained, the energy-momentum tensor of the same field confined by the same boundary in curved spacetime can be obtained too. Here the Casimir effect for a massless Dirac field in the two-dimensional RN background has been studied.…”

“…In Refs [10][11][12], Wald's axioms [13][14][15] for renormalized energy-momentum tensor were used to calculate the Casimir effect indirectly in two-dimensional curved spacetime. The massless scalar field in two-dimensional Schwarzschild black hole background [10], two-dimensional string black hole background [11], and two-dimensional Achucarro-Ortiz black hole background [12] were studied, respectively. On the one hand, as far as we know, the Casimir effect for the Dirac field in curved spacetime is yet to be studied.…”

Casimir Energy in Hartle–Hawking State

“…Employing the Wald's axioms, [12,13] Ghafarnejad and Salehi [14] derived the general form of the energy momentum tensor for the massless scalar field in twodimensional Schwarzschild-de Sitter spacetime. It was expanded to some other backgrounds by Setare [15,16] and Vagenas, [17] etc. In this Letter, we calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method and discuss its approximate expressions in the low and high temperature limits.…”