  In the light of a general scenario of a two-level non-Hermitian
$\mathcal{PT}$-symmetric Hamiltonian we apply the tetrad-based method to
analyze the possibility of analogue Hawking radiation. It is done by making use
of the conventional null-geodesic approach wherein the associated Hawking
radiation is described as a quantum tunneling process across a classically
forbidden barrier which the event horizon imposes. An interesting aspect of our
result is that our estimate for the tunneling probability is independent of the
non-Hermitian parameter that defines the guiding Hamiltonian.
