  The Kottler spacetime in isotropic coordinates is known where the metric is
time-dependent. In this paper, the 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 the Schwarzschild-(anti-)de Sitter metric. In canonical
coordinates, it is known that the unparameterized spatially projected null
geodesics of the Kottler and Schwarzschild spacetimes coincide. We show that in
isotropic static coordinates, the refractive indices of Kottler and
Schwarzschild are not proportional, yielding spatially projected null geodesics
that are different.
