  Employing the quasi-Maxwell form of the Einstein field equations in the
context of gravitoelectromagnetism, we introduce a general relativistic analog
of Poisson's equation as a natural outcome of the corresponding spacetime
decomposition formalism. The active density introduced in this formalism, apart
from the matter-energy density and pressure, includes a third component which
is the gravitoelectromagnetic energy density. This general relativistic analog
of Poisson's equation is compared with another analog introduced by Ehlers et
al. in [1]. Introduction of the cosmological constant and its effect on the
active mass, are also discussed for both exterior and interior static
spacetimes. In the stationary case, we consider the Kerr spacetime with a
special choice for its interior metric.
