2019/06/09 by Edward Anderson, Anderson, Edward · 2 citations
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Earth Systems and Cosmic Evolution #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1906.03642
openalex publication_date 2019/06/09 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Assuming Temporal and Configurational Relationalism, GR as Geometrodynamic's\nDeWitt supermetric alongside local Lorentzian Relativity with its universal\nfinite maximum propagation speed arises as one of very few options from Feeding\nFamilies through a Dirac-type Algorithm for Consistency. This amounts to\nSpacetime Construction from prior assumptions about space and dynamics alone.\nThe other alternatives, arising as cofactors' likewise strongly vanishing roots\nare, firstly, Galileo-Riemann Geometrostatics with Galilean Relativity's\ninfinte propagation speed. Secondly, Strong Gravity with Carrollian Relativity\n's zero propagation speed. If none of these vanish, constant mean curvature of\nthe spatial slice is enforced, paralleling previous work on decouping GR's\nconstraints and addressing its initial-value problem. Assuming just Temporal\nRelationalism, spatial 3-diffeomorphism Configurational Relationalism is\nenforced as an integrability as one of very few options. The alternatives here\nare, once again, Galileo-Riemann Geometrostatics and Strong Gravity, for which\nspatial 3-diffeomorphisms are thereby optional, and local volume preserving\ndiffeomorphisms. Options are few in each case above due to Rigidity kicking in.\n We furthermore demonstrate that such Rigidities are more generally Lie rather\nthan specific to Dirac-type Algorithms. We do this by deriving the conformal\nversus projective ambiguity in top-geometry by feeding the general quadratic\ngenerator into the Lie Algorithm for Consistency. Both Feeding Families through\na Brackets Consistency Algorithm and Rigidity are thus additionally of\nrelevance to the Foundations of Geometry.\n