It is reasonable to ex pect that a bound source cannot produce arbitrarily large gravitational mu ltipole moments. By observing the behavior of spacetime metric with large multipole moments at small distances from the source\, 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 the minimal size has a power law relation with m ultipole moments that is different from the analogous Newtonian scaling. W e also look at spacetimes with small deviations in quadrupole moment from the Kerr black hole and discuss the shift of gravitational wave phase for a test particle. Future space-based telescope LISA has a good prospect of constraining such small deviations in multipole moments.

\n DTSTART:20241007T173000Z LOCATION:Zoom\, Room none SUMMARY:Vacuum spacetime with multipole moments: the minimal size conjectur e and gravitational wave observables END:VEVENT END:VCALENDAR