  Using a lattice equation of state combined with the D-dimensional
Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate
the possibility of the formation of compact objects as well as the time
evolution of the scale factor and the density profile of a self-gravitating
material cluster. The numerical results show that in a $2+1$ dimensional
spacetime, the mass is independent of the central pressure. Hence, the
formation of only compact objects with a finite constant mass similar to the
white dwarf is possible. However, in a $3+1$ dimensional spacetime,
self-gravity leads to the formation of compact objects with a large gap of mass
and the corresponding phase diagram has the same structure as the one for
Neutron Star. The results also show that beyond certain critical central
pressure, the star is unstable against gravitational collapse, and it may end
in a black hole. Analysis of spacetimes of higher dimensions shows that gravity
has the stronger effect in $3+1$ dimensions. Numerical solutions of the
Friedmann equations show that the effect of the curvature of spacetime
increases with increasing temperature, but decreases with increasing
dimensionality beyond $D=3$.
