  The tidal disruption of stars by supermassive black holes (SMBHs) probes
relativistic gravity. In the coming decade, the number of observed tidal
disruption events (TDEs) will grow by several orders of magnitude, allowing
statistical inferences of the properties of the SMBH and stellar populations.
Here we analyse the probability distribution functions of the pericentre
distances of stars that encounter an SMBH in the Schwarzschild geometry, where
the results are completely analytic, and the Kerr metric. From this analysis we
calculate the number of observable TDEs, defined to be those that come within
the tidal radius $r_{\rm t}$ but outside the direct capture radius (which is,
in general, larger than the horizon radius). We find that relativistic effects
result in a steep decline in the number of stars that have pericenter distances
$r_{\rm p} \lesssim 10\,r_{\rm g}$, where $r_{\rm g} = GM/c^2$, and that for
maximally spinning SMBHs the distribution function of $r_{\rm p}$ at such
distances scales as $f_{\rm r_{\rm p}}\propto r_{\rm p}^{4/3}$, or in terms of
$\beta \equiv r_{\rm t}/r_{\rm p}$ scales as $f_{\beta} \propto \beta^{-10/3}$.
We find that spin has little effect on the TDE fraction until the very
high-mass end, where instead of being identically zero the rate is small
($\lesssim 1\%$ of the expected rate in the absence of relativistic effects).
Effectively independent of spin, if the progenitors of TDEs reflect the
predominantly low-mass stellar population and thus have masses $\lesssim
1M_{\odot}$, we expect a substantial reduction in the rate of TDEs above
$10^{7}M_{\odot}$.
