The Fastest Unbound Stars in the Universe
  The discovery of hypervelocity stars (HVS) leaving our galaxy with speeds of
nearly $10^{3}$ km s$^{-1}$ has provided strong evidence towards the existence
of a massive compact object at the galaxy's center. HVS ejected via the
disruption of stellar binaries can occasionally yield a star with $v_{\infty}
\lesssim 10^4$ km s$^{-1}$, here we show that this mechanism can be extended to
massive black hole (MBH) mergers, where the secondary star is replaced by a MBH
with mass $M_2 \gtrsim 10^5 M_{\odot}$. We find that stars that are originally
bound to the secondary MBH are frequently ejected with $v_{\infty} > 10^4$ km
s$^{-1}$, and occasionally with velocities $\sim 10^5$ km s$^{-1}$ (one third
the speed of light), for this reason we refer to stars ejected from these
systems as "semi-relativistic" hypervelocity stars (SHS). Bound to no galaxy,
the velocities of these stars are so great that they can cross a significant
fraction of the observable universe in the time since their ejection (several
Gpc). We demonstrate that if a significant fraction of MBH mergers undergo a
phase in which their orbital eccentricity is $\gtrsim 0.5$ and their periapse
distance is tens of the primary's Schwarzschild radius, the space density of
fast-moving ($v_{\infty} > 10^{4}$ km s$^{-1}$) SHS may be as large as $10^{3}$
Mpc$^{-3}$. Hundreds of the SHS will be giant stars that could be detected by
future all-sky infrared surveys such as WFIRST or Euclid and proper motion
surveys such as LSST, with spectroscopic follow-up being possible with JWST.
