An intrinsic connection of space-time points
Ty Shedleski, Muhammad Usman
TL;DR
The paper investigates whether two spacetime regions connected by an Einstein-Rosen bridge can exchange energy via quantum-field-inspired dynamics in curved spacetime. It formulates and analyzes the Klein-Gordon equation $Δ_g φ + (m^2 + ξ R) φ = 0$ and the Dirac equation $(i γ^μ ∇_μ - m) ψ = 0$ in curved backgrounds, then models a Schwarzschild-wormhole geometry with a harmonic oscillator as the matter source, solving the Einstein Field Equations $G_{μν} = (8πG/c^4) T_{μν}$ for the coupled system. Two distinct energy-transfer regimes emerge: Solution-I with asymptotically diverging oscillator momentum near the horizon, and Solution-II with smooth, damping-free transfer and finite momentum, both illustrating energy flow through the wormhole. The results offer a conceptually intriguing bridge between classical spacetime connectivity and quantum-field dynamics, hinting at energy-transfer mechanisms across causally disconnected regions in idealized gravitational settings.
Abstract
Quantum field theory (QFT) describes the dynamics of quantum particles in the quantum realm in the Minkowski space-time, whereas the General Relativity (GR) is a classical theory describing the nature of dynamical behavior of large bodies in different space-times. This research is a proposal to the proof of concept that through the Einstein-Rosen bridge (also known as wormhole) the information can travel between two points %through quantum mechanical phenomenon, Hawking radiation thus proving the classical entanglement connection between two spatially distant points which are not causally connected. These results introduce the classical entanglement between the galactic black hole with its surrounding.