Causal structure and topology change in (2+1)-dimensional simplicial gravity

Abstract

We develop a systematic method for analyzing the causal structure at vertices in (2+1)-dimensional Lorentzian simplicial gravity. By examining the intersection patterns of lightcones emanating from a vertex with its simplicial neighbourhood, we identify 13 distinct causal types of Lorentzian tetrahedra -- excluding configurations with null faces. This classification forms the basis for a topological characterization of the local causal structure in terms of the number of connected regions on the triangulated 2-sphere that are spacelike and timelike separated from a bulk vertex. These local causal data allow us to identify regular causal configurations and new types of irregular causal configurations, generalizing well-known (1+1)-dimensional topologies, such as `Trousers' and `Yarmulkes', to higher dimensions. We further investigate the dynamical implications of vertex causality by analyzing the behaviour of deficit angles and the Regge action in explicit configurations. Transitions in `vertex-causality' coincide with discontinuities in the curvature, suggesting discrete topology change. Causally irregular hinges correspond to discrete conical singularities, while vertex causal irregularities manifest as point-like singularities. Interestingly, we find that vertex and hinge causality are generally independent. These results have direct implications for discrete quantum gravity approaches where the emergence of semiclassical spacetime depends on how causal structures are encoded within the triangulation.

35 pages, 16 figures. Article now matches the published article in PRD

References in corpus (35)

• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Emergence of a 4D World from Causal Quantum Gravity
• A New Spin Foam Model for 4d Gravity
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• The causal set approach to quantum gravity
• A non-perturbative Lorentzian path integral for gravity
• Planckian Birth of the Quantum de Sitter Universe
• Discrete structures in gravity
• Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
• Effective Spin Foam Models for Four-Dimensional Quantum Gravity
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• A spin foam model for general Lorentzian 4-geometries
• Causal Dynamical Triangulations without Preferred Foliation
• Implementing causality in the spin foam quantum geometry
• Discrete gravity dynamics from effective spin foams
• Spacetime foam: a review
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Causal continuity in degenerate spacetimes
• Divergences and Orientation in Spinfoams
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Fixed-Topology Lorentzian Triangulations: Quantum Regge Calculus in the Lorentzian Domain
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Realizability of the Lorentzian (n,1)-Simplex
• Lorentzian quantum cosmology from effective spin foams
• Tensor network approach to 2d Lorentzian quantum Regge calculus
• De Sitter horizon entropy from a simplicial Lorentzian path integral
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Causal structure in spin-foams
• Geometry from local flatness in Lorentzian spin foam theories
• Partial absence of cosine problem in 3d Lorentzian spin foams
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality