The prospect of distinguishing astrophysical objects with LISA

The famous no-hair theorem dictates that the multipole moments of Kerr black holes depend only on their mass and angular momentum. Thus, the measurement of multipole moments of astrophysical objects through gravitational-wave observations provides a novel way to test the theorem and distinguish black holes from other astrophysical objects. This paper studies the gravitational wave radiation from an extreme mass ratio inspiral system consisting of a supermassive Kerr black hole and a spinning stellar-mass compact object. The quadrupolar moment induced by the rotation of the stellar-mass object carries information about its internal structure. We show that the Laser Interferometer Space Antenna (LISA) can probe the imprints of quadrupolar deformation for certain astrophysical objects and thus provide a way to identify them.