Stress and Geometry for Isotropic Singularities
arXiv:2310.19269 · doi:10.1103/PhysRevLett.133.011401
Abstract
We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general relativistic stress-energy tensors. Their leading behaviors are dictated by an initial hypersurface conformal embedding. We also show that an isotropic Big Bang determines a canonical non-singular metric on and about the initial hypersurface as well as a cosmological time. This assigns a volume and energy to the initial point singularity.
6 pages, LaTeX, minor corrections
References in corpus (17)
- Aspects of Holographic Entanglement Entropy
- Gauge Invariances and Phases of Massive Higher Spins in (A)dS
- Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
- Isotropic cosmological singularities 2: The Einstein-Vlasov system
- Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations
- Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes
- Causal structures and causal boundaries
- Isotropic cosmological singularities: other matter models
- Weyl Invariance and the Origins of Mass
- Stable Big Bang formation for Einstein's equations: The complete sub-critical regime
- Renormalized Volume
- Yang-Mills detour complexes and conformal geometry
- Isotropic cosmological singularities in spatially-homogeneous models with a cosmological constant
- Conformal boundary operators, T-curvatures, and conformal fractional Laplacians of odd order
- Stability of AVTD Behavior within the Polarized -symmetric vacuum spacetimes
- Higher fundamental forms of the conformal boundary of asymptotically de Sitter spacetimes
- Bach equation and the matching of spacetimes in conformal cyclic cosmology models