  We derive here the metric for Einstein's static universe (ESU) directly from
Einstein equation, i.e., by considering both $G_{ik}$ and $T_{ik}$. We find
that in order that the fluid pressure and acceleration are {\em uniform} and
finite despite the presence of a coordinate singularity, the effective density
$\rho_e = \rho + \Lambda/8 \pi =0$, where $\Lambda$ is the cosmological
constant. Under weak energy condition, this would imply $\rho = \Lambda =0$ for
ESU. This means that if one would need to invoke a source of ``repulsive
gravity'' in some model, (i) the model must be non-static, (ii) the repulsive
gravity must be due to a ``quintessence'' or a ``dark energy'' fluid with
negative pressure and appear on the right hand side (RHS) of the Einstein
equation through $T_{ij}$ rather than through a fundamental constant residing
on the LHS of the same equation, and (iii) energy density of both normal matter
and the ``dark energy fluid'' should be time dependent. In fact, the repulsive
gravity would be due to a time independent $\Lambda$, it would be extremely
difficult to understand why the associated energy density should be
approximately $10^{120}$ times lower than the value predicted by quantum
gravity. On the other hand, for a dark energy fluid whose energy density is
time dependent, it would be much easier to understand such an extremely low
present energy density: the original initial value of the energy density of the
fluid could be equal to the quantum gravity value while the present low value
is due to decay with time.
