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Conformal field theories can exchange energy through a boundary interface.
Imposing conformal boundary conditions for static interfaces implies energy
conservation at the interface. Recently, the reflective and transmitive
properties of such static conformal interfaces have been studied in two
dimensions by scattering matter at the interface impurity. In this note, we
generalize this to the case of dynamic interfaces. Motivated by the connections
between the moving mirror and the black hole, we choose a particular profile
for the dynamical interface. We show that a part of the total energy of each
side will be lost in the interface. In other words, a time-dependent interface
can accumulate or absorb energy. While, in general, the interface follows a
time-like trajectory, one can take a particular limit of a profile
parameter($\beta$), such that the interface approaches a null line
asymptotically$(\beta\rightarrow 0)$. In this limit, we show that for a class
of boundary conditions, the interface behaves like a `semipermeable membrane'.
We also consider another set of conformal boundary conditions for which, in the
null line limit, the interface mimics the properties expected of a horizon. In
this case, we devise a scattering experiment, where (zero-point subtracted)
energy from one CFT is fully transmitted to the other CFT, while from the other
CFT, energy can neither be transmitted nor reflected, i.e., it gets lost in the
interface. This boundary condition is also responsible for the thermal energy
spectrum which mimics Hawking radiation. This is analogous to the black hole
where the horizon plays the role of a one-sided `membrane', which accumulates
all the interior degrees of freedom and radiates thermally in the presence of
quantum fluctuation. Stimulated by this observation, we comment on some
plausible construction of wormhole analogues.