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The Galactic Center has been under intense scrutiny in the recent yearsthanks to the unprecedented missions aiming at measuring the gas and stardynamics near the supermassive black hole (SMBH) and at finding gravitationalwave (GW) signatures of inspiralling stellar black holes. In the crowdedenvironment of galactic nuclei, the two-body interactions alter thedistribution of stars on long timescales, making them drift in energy andangular momentum. We present a simplified analytical treatment of thescattering processes in galactic stellar nuclei, assuming all stars have thesame mass. We have discussed how the interplay between two-body relaxation andgravitational wave emission modifies the slope of the inner stellar cusp withinthe SMBH sphere of influence, and calculated the rates of tidal disruptionevents (TDEs) and main-sequence extreme-mass ratio inspirals (MS-EMRIs) ofstars that are tidally disrupted by the SMBH. We find that typically the ratioof the TDE and MS-EMRI rates is the square of the ratio of the tidal andSchwarzschild radii. For our Galaxy, this implies that the rate of MS-EMRIs isjust about a percent of the TDE rate. We then consider the role of starsinjected on highly eccentric orbits in the vicinity of the SMBH due to Hillsbinary disruption mechanism, and show that the MS-EMRI rate can almost approachthe TDE rate if the binary fraction at the SMBH influence radius is close tounity. Finally, we discuss that physical stellar collisions affect a large areaof phase space.

Tidal disruption events, main-sequence extreme-mass ratio inspirals and binary star disruptions in galactic nuclei