  In this paper, the geometric properties of the conformal metric are studied
and its exact solution of the geodesic deviation equation is presented. We also
find out the stress-energy tensor of this geometry and compare it with the
usual prefect-fluid case, obtaining an equation of state as $P =
-\frac{1}{3}\rho$ in 4D space-time dimension. Finally, the low-energy regime of
the metric is studied, in which we obtain the stress-energy tensor proportional
to the projection tensor.
