Extracting High-Order Multipole Moments of Asymptotically Flat, Stationary, and Axisymmetric Bodies

Multipole moments of solutions to the Einstein equations provide insights into the physical characteristics of gravitational sources, such as their shape and mass distribution. Our work extends the framework for extracting Geroch-Hansen multipole moments from gravitational waves emitted by compact objects spiraling into massive, stationary, and axisymmetric bodies, following the approach developed by Ryan. We computed the orbital energy loss of the inspiraling object due to the emission of gravitational waves in terms of the multipole moments of the central body up to the seventh mass-current multipole. The result can be used to extract multipole moments of any asymptotically flat, stationary, and axisymmetric spacetime, regardless of the choice of coordinate system. One key application of our extended analysis is extracting higher-order multipole moments from highly-accurate, Hartle-Thorne solutions of slowly rotating neutron stars. These higher-order moments are useful for exploring potential no-hair-like relations for neutron stars, which will help resolve parameter degeneracies in future observations. Work is being done to add these moments into the open-source MUSES module called QLIMR.