The Galactic Centre contains populations of stellar-mass andsubstellar-mass compact objects orbiting the central black hole,classified as early extreme-mass ratio inspirals (E-EMRIs) and extremelylarge mass ratio inspirals (XMRIs). These systems constitute asymmetricbinaries, characterized by mass ratios exceeding 10,0000 to 1. This massdifferential causes the secondary body to approximate a test particle,completing tens of thousands or millions of orbital cycles prior tocoalescence. This high cycle count delineates the spacetime geometry andmultipolar structure of the central black hole with greater resolutionthan comparable-mass supermassive black hole binaries, which undergorapid coalescence and exhibit fewer in-band cycles. The prolongedorbital data can in principle also facilitate topological analysis. Byapplying the Gauss-Bonnet theorem, the accumulated orbital precessionparameters relate the integrated curvature of the spacetime to itstopological invariants. The continuous gravitational wave emission fromthese populations generates a non-Gaussian, non-stationary compositesignal within the frequency band of the Laser Interferometer SpaceAntenna. This aggregated signal comprises an incoherent superposition ofindividual waveforms from eccentric and circular orbits, whichsuperimposes upon the spectral signatures of other target sources,including binaries of supermassive black holes and verificationbinaries. Spectral analysis indicates that sources with minimalfrequency drift constitute an unresolved stochastic background, whilesystems with measurable frequency evolution produce distinct spectralcomponents. Extracting targeted signals from this composite datarequires time-frequency domain modeling and non-Poissonian statisticalsubtraction protocols.
