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Motivated by an improved multi-wavelength observational coverage of thetransient sky, we investigate the importance of relativistic effects indisruptions of stars by non-spinning black holes (BHs). This paper focuses oncalculating the ballistic rate of return of debris to the black hole as thisrate is commonly assumed to be proportional to the light curve of the event. Wesimulate the disruption of a low mass main sequence star by BHs of varyingmasses ($10^5,10^6,10^7 M_\odot$) and of a white dwarf by a $10^5 M_\odot$ BH.Based on the orbital energy as well as angular momentum of the debris, we inferthe orbital distribution and estimate the return rate of the debris followingthe disruption. We find two signatures of relativistic disruptions: a gradualrise as well as a delayed peak in the return rate curves relative to theirNewtonian analogs. Assuming that the return rates are proportional to the lightcurves, we find that relativistic effects are in principle measurable given thecadence and sensitivity of the current transient sky surveys. Accordingly,using a simple model of a relativistic encounter with a Newtonian parametricfit of the peak leads to an overestimate in the BH mass by a factor of $\sim{\rm few}\times0.1$ and $\sim {\rm few}$ in the case of the main sequence starand white dwarf tidal disruptions, respectively.

Tidal disruption of a star in the Schwarzschild spacetime: relativistic effects in the return rate of debris