  A static spacetime with no centrifugal repulsion, previously studied by
Dadhich, is investigate in this paper. The source of curvature is considered to
be an anisotropic fluid with $\rho = -p_{r}$ and constant angular pressures.
The positive parameter from the line-element is interpreted as the invariant
acceleration of a static observer. The timelike and null geodesics of the
spacetime are examined. A regularized form of the metric is proposed, rendering
it finite at the origin. The energy density of the fluid becomes finite and
negative for any $r$ and all the pressures are positive throughout the
spacetime. The Tolman-Komar energy $W(r)$ is computed and proves to be smaller
than that one calculated with the Dadhich metric.
