Casimir effect for scalar field rotating on a disk

We compute the vacuum energy of a scalar field rotating with angular velocity $\Omega$ on a disk of radius $R$ and with Dirichlet boundary conditions. The rotation is introduced by a metric obtained by a Galilean transformation from a rest frame. The constraint $\Omega R<c$ must be obeyed to maintain causality. To compute the vacuum energy, we use an imaginary frequency representation and the well-known uniform asymptotic expansion of the Bessel function. We use the zeta-functional regularization and separate the divergent contributions, which we discuss in terms of the heat kernel coefficients. The divergences are found to be independent of rotation. The renormalized finite part of the vacuum energy is negative and becomes more negative for larger rotation frequencies.