On a modified Rindler geometry

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.