Exact Coupling Of Event Horizons In Curved Spacetime Heterostructures. Application To Black-Hole Physics

TL;DR

This paper develops a theoretical framework for quantum transport across coupled black-hole horizons in curved spacetime, deriving key quantities like self-energy and Green's functions, and explores implications for wormholes and quantum analogues.

Contribution

It introduces a novel application of generalized Klein-Gordon equations to model black-hole horizon coupling and quantum transport in curved spacetime heterostructures.

Findings

Derived the coupling self-energy for black-hole horizons.

Calculated surface Green's functions and entropy.

Formulated nonequilibrium transport equations for black-hole radiation.

Abstract

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.