Models of Spacetime – II: Dynamical Metric  

Einsteinian Model > s.a. causality; complex; cosmological models; embeddings; types of metrics and spacetimes.
* Idea: An equivalence class of Lorentzian manifolds under (active) diffeomorphisms.
* Background stucture: Top and diff (not, e.g., time); Spacetime is a 4D connected, Cinfty Hausdorff manifold; Notice that E Cassirer tried to negotiate between Kant's and Einstein's positions by saying that the spacetime topology is a priori, while the metric is subject to empirical evidence.
* Dynamical stucture: A C2 (or C1,+) time-oriented metric of lorentzian signature, obeying the Einstein equation.
@ Mathematical: Busemann 67; Pimenov 68.
@ Algebraic description: Geroch CMP(72) [Einstein algebras]; Yodzis PRIA(75); Heller IJTP(92); Akofor a0907.
@ Axiomatic: Penrose essay(66); Ehlers et al in(72); Woodhouse JMP(73); Schröter RPMP(88), & Schelb RPMP(92); Borchers & Sen CMP(90); Rau pr(90); Rodrigues et al FPL(90); Audretsch & Lämmerzahl JMP(91), in(95); Covarrubias IJTP(93); Schelb IJTP(97) [Weyl vs Lorentz structrure]; Nikolic gq/99 [space-time distinction]; Lämmerzahl GRG(01)gq; Kopf & Paschke mp/01-in; Schröter gq/07, gq/07, gq/07; Sánchez-Rodríguez AIP(08)-a0803 [geometrical structures]; Krasnikov PRD(09)-a0903 [hole-free spacetimes].
@ Newtonian limit: Ehlers CQG(97).
@ Dimension: Lämmerzahl & Macías JMP(93); Tegmark CQG(97)gq [and strings]; Borstnik & Nielsen JPA(02) [why 3+1]; Ghaboussi gq/03 [??]; Rama PLB(07) [reason, from strings]; Wesson a0712-in [conceptual]; Caruso a0806 [3+1 and anthropic arguments]; Maziashvili PLB-a0809, a0905-GRF [running]; Bojowald in(07)-a0807 [and canonical gravity]; > s.a. quantum spacetime.
@ Dimensional reduction: Svozil JPA(86) [fractals and dimensional shadowing]; Manogue & Dray MPLA(99)ht/98 [without compactification]; Cognola & Zerbini NPB(01); Pons JPCS(07)ht/06 [truncation, constraints and consistency]; Maraner & Pachos AP(08)-a0704 [from breaking of general covariance].
@ Signature: van Dam & Ng PLB(01)ht; Wetterich ht/04, Darabi gq/04 [spontaneous symmetry breaking]; Yahalom FP(08)gq/06 [from stability]; > s.a. modified electromagnetic theory.
@ Related topics: Segal in(88); Audretsch & Lämmerzahl GRG(95) [conformal structure]; Cassa JGP(96) [from world-lines]; Anderson gq/99 [no need for metric]; Bernal et al FP(02)gq/00 [clocks and rods]; Pauri & Vallisneri gq/02-in [identifying points]; Mitra gq/05 [and dark matter + dark energy]; Jonsson AJP(05)mar-a0708 [visualizing]; Anderson SHPMP(07) [3-space geometrodynamics without spacetime]; Bel a0711 [global structure and meaning]; Madarasz et al a0709 [time dilation and equivalence principle]; Fernández & Rodrigues a0909 [as plastic distortion of Lorentz vacuum]; > s.a. Hole Argument; Splitting Theorem.
> Related topics: see boundaries; Chronogeometry; Compactification; metric decomposition and matching; general relativity; lorentzian geometry [analogs].

Classical Generalizations > s.a. branes; kaluza-klein theory; lorentz symmetry violations; special relativity; torsion.
* Types: Violations of Lorentz symmetry; More general structures than Lorentzian manifold ( signature change, degenerate metrics, Finsler geom, ...); Higher-dimensional (unified theories); Small-scale topology.
@ References: Hájícek JMP(71) [non-Hausdorff]; Caccese et al gq/99 [and inertia]; Duan & Li JMP(98)ht, Li CQG(01)gq/99 [with disclinations].
> Other types: see finsler geometry; modified general relativity [signature change].

Quantum Models and Other Fundamental Aspects > s.a. discrete and quantum spacetime.
@ Spacetime as emergent: Hu IJTP(05)gq, gq/06-in [condensate]; Pirogov gq/05-in, gq/05-in; Seiberg ht/06-in; Dreyer in(08)gq/06; Weinfurtner a0711-PhD [motivated by analog gravity]; Visser a0712-in ["rainbow geometry", pedagogical examples]; Weinfurtner et al PoS-a0804; Volovik PTRS(08)-a0801 [Fermi-point scenario]; Yang IJMPA(08)-a0803 [and the cosmological constant]; > s.a. approaches to quantum gravity [group field theory] and spacetime geometry in quantum gravity.
@ And logic: Madarasz et al in(06)gq [and first-order logic]; Uckelman & Uckelman SHPMP(07) [modal and temporal logics for abstract spacetime structures].
@ Related topics: Finkelstein & Rodriguez PhyD(86) [levels of description and structures]; Finkelstein IJTP(99) [unification with dynamical laws]; Nakanishi ht/06 [in ultimate theory]; & H B Nielsen; > s.a. non-dynamical models.

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