Models
of Spacetime – II: Dynamical Metric| 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).
@ 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 a0803-in
[geometrical structures].
@ 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].
@ Dimensional reduction: Svozil JPA(86) [fractals and dimensional shadowing];
Manogue & Dray MPLA(99)ht/98 [without
compactification]; Cognola & Zerbini NPB(01);
Pons ht/06 [truncation,
constraints and consistency]; Maraner & Pachos 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)-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]; > 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;
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 gq/06-in;
Weinfurtner a0711-PhD
[motivated by analog gravity]; Visser a0712-in
["rainbow geometry", pedagogical examples]; Weinfurtner et al a0804-in;
Volovik a0801-in
[Fermi-point scenario]; Yang a0803-in
[and the cosmological constant]; > s.a. approaches
to quantum gravity [group field theory].
@ And logic: Madarasz et al gq/06-in
[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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Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008