  In this work, we explicitly construct the vacuum solution of Einstein's
equations with prescribed multipole moments. By observing the behavior of the
multipole spacetime metric at small distances, we conjecture that for a
sufficiently large multipole moment, there is a minimal size below which no
object in nature can support such a moment. The examples we have investigated
suggest that such minimal size scales as $(M_n)^{1/(n+1)}$ (instead of
$(M_n/M)^{1/n}$), where $M$ is the mass and $M_n$ is the $n$th order multipole
moment. With the metric of the "multipole spacetime", we analyze the shape of
black hole shadow for various multipole moments and discuss the prospects of
constraining the moments from shadow observations. In addition, we discuss the
shift of gravitational wave phase with respect to those of the Kerr spacetime,
for a test particle moving around an object with this set of multipole moments.
These phase shifts are required for the program of mapping out the spacetime
multipole moments based on gravitational wave observations of extreme
mass-ratio inspirals.
