  There is a well-known correspondence between the physics of black hole
evaporation and that of moving mirrors in QFT. However, most analyses in this
subject rely on prescribed mirror trajectories. Here, we study the flat-space
dynamics of $1+1$-dimensional Conformal Field Theories interacting with a
relativistic boundary particle of mass $m$ acting as a perfect mirror. The
trajectory of the latter is not fixed but follows its own relativistic equation
of motion $F^\mu=ma^\mu$. For given initial conditions at past null infinity,
we find the boundary particle's trajectory and the reflected energy-momentum of
the quantum fields. For incoming vacuum states, the solution yields mirror
orbits that correspond to extremal black holes. For the class of incoming
states that produce orbits becoming null in finite proper time -- corresponding
to the formation of a horizon -- at the classical level, the quantum
backreaction avoids this endpoint rendering the mirror's velocity in lightcone
coordinates finite. We investigate the behavior of the Averaged Null Energy
Condition, which in this setup reduces to a boundary term.
