  Following a previous idea, a curved geometry is proposed as being valid in
accelerated systems, in Minkowski space. The curvature turns out to be
generated by the source of the accelerated motion. An exponential factor
depending on $\rho$ (the coordinate along the acceleration) and a constant
length is introduced in the metric. The source stress tensor appears to
represent an imperfect fluid with zero energy density but nonzero tangential
pressures which do not depend on Newton's constant even for $\rho>>l_{p}$,
where $l_{p}$ is the Planck length. The Komar mass is proportional to the
constant acceleration $g$ and it does not depend on the choice of the value of
the constant $k$ from the exponential factor. Null and timelike geodesics along
the $\rho$ direction are investigated. A slight change in the metric leads to
nonzero energy density and pressure along the acceleration direction, with all
the energy conditions being satisfied far from the Planck world.
