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Vacuum spacetime with multipole moments: the minimal size conjecture and gravitational wave observables

Shammi Tahura, PhD; University of Iowa

It is reasonable to expect that a bound source cannot produce arbitrarily large gravitational multipole 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 multipole moments that is different from the analogous Newtonian scaling. We 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. 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.