  Recently we have discussed the generalized parametrized Klein-Gordon equation
for curved spacetime. We have also discussed its derivation from several
approaches, the direct Feynman parametrization, the state function entropy or
equivalently the information theory approach, and the stochastic differential
equation approach. We have even suggested a generalization of the statistics of
the entropy to the generalized entropies and derived the particular
nonextensive statistics parametrized Klein-Gordon equation, and discussed its
nonlinear FPE replacement of the complicated Gibbs-Boltzmann statistics entropy
derived analog with complicated nonlinear potential or drift and diffusion
coefficients. In this article we apply these previously derived results to the
quantum transport in abruptly coupled curved space-time heterostructures,
applied here specifically to Black-Hole event horizon coupling to normal curved
space-time. We derive the coupling self energy, and the Garcia-Molliner surface
Green's functions from which we can calculate the surface area and entropy. We
then derive the nonequilibrium transport equations for the radiation from the
Black-Hole. We discuss the theory application to Worm Holes and quantum
analogues.
