Geometry-information duality: Quantum entanglement contributions to gravitational dynamics

Abstract

We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields, specifically through the entanglement entropy of quantum states. By establishing a correspondence between geometric invariants and informational measures, we introduce an informational stress–energy tensor Tμνinfo, derived from quantum entanglement entropy, into Einstein's field equations. This framework modifies spacetime geometry, particularly in regimes of strong gravitational fields, such as near black holes. Our approach provides explicit corrections to Newton's constant G, incorporating entanglement entropy contributions from various quantum fields with explicit dependence on fundamental constants ħ, c, and kB, ensuring dimensional consistency. These corrections have implications for black hole thermodynamics, leading to entropy and temperature modifications, and extend to cosmology, influencing inflationary dynamics, Big Bang nucleosynthesis, and the nature of dark energy. Our findings suggest that quantum information fundamentally shapes spacetime structure, offering testable predictions in gravitational and cosmological phenomena and shedding new light on challenges in quantum gravity.