The Extended Einstein Field Equations: A Path to Quantum Gravity

This thesis introduces an extension to the Einstein Field Equations by incorporating quantum informational measures, specifically entanglement entropy and quantum complexity, into the gravitational framework. This approach aims to bridge the gap between general relativity and quantum mechanics, offering a unified theory that integrates the geometric structure of spacetime with the principles of quantum information. The extended field equations derived in this work remain consistent with both classical general relativity and quantum information theory. This novel formulation provides potential solutions to the black hole information paradox and offers new insights into the nature of dark energy. Our investigation reveals unexpected findings, implying the role of quantum complexity in driving cosmic inflation and the emergence of classical spacetime from quantum entanglement patterns. Through perturbative and non-perturbative analyses, we explore quantum corrections to classical gravitational solutions, modified particle motion equations, and new perspectives on black hole thermodynamics and cosmological evolution. Notably, this study suggests that entanglement entropy may influence large-scale structure formation and that quantum informational terms might naturally explain the universe's late-time acceleration. The thesis also proposes observable predictions, such as unique signatures in gravitational wave observations and cosmological data, to guide future experimental tests of this framework. By investigating how gravity and quantum information interact, this work sheds light on how spacetime might emerges from quantum properties, offering a comprehensive framework for exploring quantum gravity.