  Kottler spacetime in isotropic coordinates is known where the metric is
time-dependent. In this paper, Kottler spacetime is given in isotropic static
coordinates (i.e., the metric components are time-independent). The metric is
found in terms of the Jacobian elliptic functions through coordinate
transformations from Schwarzschild-(anti-) de Sitter metric. In canonical
coordinates, it is known that the spatially projected null geodesics of Kottler
and Schwarzschild spacetimes coincide. We show that the refractive indices of
Kottler and Schwarzschild are not proportional, yielding spatially projected
null geodesics that are different. For $\Lambda<0$, the index of refraction can
be found asymptotically, since the spacetime is conformally compactified.
