2018/08/31 by A. Stern, Chuang Xu
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Commutative property #Computer science #Cosmology and Gravitation Theories #Geometry #Gravitational singularity #Limit (mathematics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Signature (topology) #Singularity #Space (punctuation) #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.98.086015
published as Phys. Rev. D 98, 086015 (2018) · 30 pages, 8 figures
openalex publication_date 2018/10/12 · arxiv created 2018/10/18 · arxiv updated 2018/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Various classical solutions to lower dimensional Ishibashi-Kawai-Kitazawa-Tsuchiya--like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature change is found to be a common feature of these manifolds when quadratic and cubic terms are included in the bosonic action. In fact, a single manifold may exhibit multiple signature changes. Regions with a Lorentzian signature may serve as toy models for cosmological spacetimes, complete with cosmological singularities, occurring at the signature change. The singularities are resolved away from the commutative limit. Toy models of open and closed cosmological spacetimes are given in two and four dimensions. The four-dimensional cosmologies are constructed from noncommutative complex projective spaces, and they are found to display a rapid expansion near the initial singularity.