  We consider collisions between stars moving near the speed of light around
supermassive black holes (SMBHs), with mass
$M_{\bullet}\gtrsim10^8\,M_{\odot}$, without being tidally disrupted. The
overall rate for collisions taking place in the inner $\sim1$ pc of galaxies
with $M_{\bullet}=10^8,10^9,10^{10}\,M_{\odot}$ are $\Gamma\sim5,0.07,0.02$
yr$^{-1}$, respectively. We further calculate the differential collision rate
as a function of total energy released, energy released per unit mass lost, and
galactocentric radius. The most common collisions will release energies on the
order of $\sim10^{49}-10^{51}$ erg, with the energy distribution peaking at
higher energies in galaxies with more massive SMBHs. Depending on the host
galaxy mass and the depletion timescale, the overall rate of collisions in a
galaxy ranges from a small percentage to several times larger than that of
core-collapse supernovae (CCSNe) for the same host galaxy. In addition, we show
example light curves for collisions with varying parameters, and find that the
peak luminosity could reach or even exceed that of superluminous supernovae
(SLSNe), although with light curves with much shorter duration. Weaker events
could initially be mistaken for low-luminosity supernovae. In addition, we note
that these events will likely create streams of debris that will accrete onto
the SMBH and create accretion flares that may resemble tidal disruption events
(TDEs).
