  While driven interacting quantum matter is generically subject to heating and
scrambling, certain classes of systems evade this paradigm. We study such an
exceptional class in periodically driven critical (1 + 1)-dimensional systems
with a spatially modulated, but disorder-free time evolution operator. Instead
of complete scrambling, the excitations of the system remain well-defined.
Their propagation is analogous to the evolution along light cones in a curved
space-time obtained by two Schwarzschild black holes. The Hawking temperature
serves as an order parameter which distinguishes between heating and
non-heating phases. Beyond a time scale determined by the inverse Hawking
temperature, excitations are absorbed by the black holes resulting in a
singular concentration of energy at their center. We obtain these results
analytically within conformal field theory, capitalizing on a mapping to
sine-square deformed field theories. Furthermore, by means of numerical
calculations for an interacting XXZ spin-1/2 chain, we demonstrate that our
findings survive lattice regularization.
