On the Complexified Spacetime Manifold Mapping of AdS to dS

TL;DR

This paper explores a complex manifold approach to connect anti-de Sitter and de Sitter spacetimes through analytic continuation, preserving key invariants and unitarity, and employing holographic principles to deepen understanding of quantum gravity.

Contribution

It introduces a novel complexified geometric framework unifying AdS and dS spacetimes, maintaining unitarity and invariants, and applying holographic principles to quantum gravity.

Findings

Preserves geometric invariants during AdS-dS transition

Maintains bulk unitarity for both AdS and dS

Uses holographic principles to connect entanglement and black hole entropy

Abstract

In a complex manifold, one can bridge anti-de Sitter and de Sitter spacetimes via analytic continuation, preserving geometric invariants and regularity, avoiding singularities during the AdS-dS transition. It unifies gravitational and gauge interactions under a complexified symmetry group, maintaining bulk unitarity for both AdS and dS. Boundary unitarity is upheld in AdS but not in dS due to the spacelike conformal boundary. The theory uses holographic principles like the MacDowell-Mansouri and Quantum Extremal Surface prescriptions to align entanglement and black hole entropy with AdS/CFT and general relativity. HUFT provides insights into AdS and dS holography, the cosmological constant, and quantum gravity unitarity and entanglement.