  We obtain equilibrium solutions for rotating compact stars including the
special relativistic effects. The gravity is assumed to be Newtonian, but we
used the active mass density, which takes into account all the energies such as
motions of the fluids, internal energy, pressure energy in addition to the rest
mass energy, in computing the gravitational potential using Poisson's equation.
Such a treatment could be applicable to the neutron stars with relativistic
motions or relativistic equation of state. We applied the Hachisu's
self-consistent field (SCF) method to find spheroidal as well as toroidal
sequences of equilibrium solutions. Our solutions show better agreement than
Newtonian relativistic hydrodynamic approach that does not take into account
the active mass, with general relativistic solutions. The physical quantities
such as the peak density, equatorial radii of our solutions agree with general
relativistic ones within 5%.Therefore our approach can be a simple alternative
to the fully relativistic one when large number of model calculations are
necessary as it requires much less computational resources.
