2025/04/08 by Qiaoyin Pan, Pan, Qiaoyin
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2504.06428
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we present a geometrical reconstruction of the critical points of the spinfoam amplitude for a 4D Lorentzian model with a non-zero cosmological constant. By establishing the correspondence between the moduli space of \rm SL(2,ℂ) flat connections on the graph-complement 3-manifold S3\backslash Γ5 and the geometry of a constantly curved 4-simplex, we demonstrate how the critical points encode discrete curved geometries. The analysis extends to 4-complexes dual to colored graphs, aligning with the improved spinfoam model recently introduced. Central to this reconstruction are translating the geometry of constantly curved 4-simplices into Fock-Goncharov coordinates and spinors, which translate the geometry data into holonomies and symplectic structures, thereby defining the critical points of the spinfoam amplitude. This framework provides an algorithmic foundation for computing quantum gravity corrections and opens avenues for applications in quantum cosmology and black hole physics, where the cosmological constant plays a pivotal role.