Lorentz violating scalar Casimir effect for a D-dimensional sphere

We investigate the Casimir effect, due to the confinement of a scalar field in a D-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by an additional term lambda(u center dot partial derivative phi) in the scalar field Lagrangian, where the parameter lambda and the background vector u(mu) codify the breakdown of Lorentz symmetry. We compute, as a function of D > 2, the Casimir stress by using Green's function techniques for two specific choices of the vector u(mu). In the timelike case, u(mu) = (1, 0, ...,0), the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor (1 + lambda)(-1/2). For the radial spacelike case, u(mu) = (0, 1, 0, ..., 0), we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value lambda(c) = lambda(c)(D) at which the Casimir stress transits from a repulsive behavior to an attractive one for any D > 2. The physically relevant case D 1/4 3 is analyzed in detail where the critical value lambda c vertical bar(D=3) = 0.0025 was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of D.