The Semiclassical Approximation: Its Application to Holography and the Information Paradox

In this research, we explore the semiclassical approximation to canonical quantum gravity and how a classical background emerges from the Wheeler-DeWitt (WDW) states. By employing the Wigner functional analysis, we derive the backreacted Einstein-Hamilton-Jacobi equation as an approximation to the WDW equation, along with the requisite validity conditions. We then apply this understanding to both AdS/CFT and dS/CFT correspondences in conjunction with Cauchy slice holography, to explain how the bulk is encoded in the correlation functions of the dual field theory. We then explain an appropriate description for scenarios in which gravity behaves quantum mechanically in certain regions of spacetime and explain its relation to subregion holography. We derive the validity conditions for gravity to be semiclassical near any co-dimension 1 time-like surface and employ these conditions to explore the black hole information paradox. Our analysis suggests that for evaporating black holes, there might be a violation of semiclassical gravity in the near-horizon region close to the Page time, although this is contingent upon certain assumptions. This also provides insights into the fate of information trapped within evaporating black holes. We then explore this issue from the perspectives of both external and infalling observers. We then explain how to employ the framework of Cauchy slice holography to study the retrieval of information from evaporating black holes, presenting a comprehensive approach to tackle this complex issue in quantum gravity.