Teleparallel Structures and Gravity Theories  

In General > s.a. gravitation / Riemann-Cartan Structure; stress-energy pseudotensors; Weitzenböck Connection.
* Teleparallel structure: A (parallelizable) manifold with a tetrad field (of orthonormal vectors in the Lorentzian sense) from which a flat connection with non-vanishing torsion is defined (the Weitzenböck connection), in addition to a metric as usual; An example of Riemann-Cartan structure.
* Teleparallel equivalent of general relativity: An alternative formulation of Einstein's equation, in which the gravitational field is described by the torsion of the curvature-free Weitzenböck connection of a teleparallel structure (rather than the curvature of the torsion-free connection of general relativity); A gauge theory for the translation group, which describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction.
* History: Originally proposed by Einstein in an attempt to unify gravity and electromagnetism; Now studied as a theory of gravity in its own right.
@ Teleparallel structures: Itin gq/00-MG9 [as combinations of Riemannian and symplectic structures?].
@ Reviews, intros: de Andrade et al gq/00-MG9; Garecki a1010-proc; Aldrovandi & Pereira 13; Pereira a1302-ch; Maluf AdP(13)-a1303; Aldrovandi & Pereira CH-a1506; Golovnev a1801-proc.
@ General references: Mielke AP(92) [Ashtekar-like variables]; Maluf & Kneip JMP(97)gq/95 [energy density]; Aldrovandi et al BJP(04)gq/03-conf [peculiarities of the theory]; Salgado NCB(06) [and Einstein-Hilbert action]; Belo et al ASTP-a1108 [gauge transformations]; Golovnev et al CQG(17)-a1701 [Lorentz breaking and covariance]; Hohmann et al PRD(18)-a1711 [and non-linear electrodynamics]; Krššák et al CQG(19)-a1810 [fully invariant approach]; Bejarano et al Univ(19)-a1905 [covariance]; Emtsova et al a1910 [conserved currents and superpotentials].
@ And general relativity: Knox SHPMP(11); Combi & Romero AdP(18)-a1708 [inequivalence].
@ Cosmological models: Sharif & Amir GRG(06)gq [Friedmann solutions, Lewis-Papapetrou]; de Haro & Amorós PRL(13)-a1211 [non-singular]; Järv & Toporensky PRD(16)-a1511 [with scalar field, general relativity as an attractor]; Hohmann IJGMP-a2008 [classification]; > s.a. bianchi I models.
@ Other solutions: Maluf & Kneip JMP(97)gq/95 [conical defects]; Nashed gq/05 [axisymmetric]; Nashed MPLA(06) [Reissner-Nordström solutions], gq/06 [charged, spherical]; > s.a. black holes; gödel solution; schwarzschild spacetime; spherical solutions; wormhole solutions.
> Online resources: see eNotes page; Wikipedia page.

Hamiltonian Formulation
* Gauge transformations: Because the flat connection introduces a notion of absolute parallelism, the theory does not have a Lorentz gauge symmetry, but it can be seen as a gauge theory of the translation group.
@ General references: Maluf JMP(94), GRG(96); Blagojević & Nikolić PRD(00)ht; Blagojević & Vasilić CQG(00)ht [gauge symmetries], PRD(01)ht/00 [conservation laws]; Maluf & da Rocha-Neto GRG(99)gq/98, PRD(01)gq/00; Sousa & Maluf PTP(00); Chee et al gq/01; Pimentel et al NCB(05)gq/04 [Hamilton-Jacobi approach]; Okołów & Świeżewski CQG(12)-a1111; Okołów GRG(13)-a1111, GRG(14) [ADM-like formulation]; Ferraro & Guzmán PRD(16)-a1609; Formiga a2004 [meaning of torsion]; Blixt et al a2012 [rev].
@ Energy, positivity: Mielke PRD(90); Chee PRD(03)gq/04 [self-dual].
@ Energy, specific solutions: Maluf & Kneip gq/95 [Kerr]; Maluf & da Rocha-Neto JMP(99)gq/98 [Bondi metric, static limit]; da Rocha-Neto & Castello-Branco JHEP(03)gq/02 [Kerr and Kerr-AdS]; Nashed MPLA(07)gq/06 [Kerr-Newman]; Sharif & Jawad MPLA(10)-a1002 [black holes with non-linear electrodynamics source].
@ Energy-momentum: Maluf GRG(98)gq/97, de Andrade et al PRL(00) [density]; Maluf et al PRD(02)gq; Maluf AdP(05)gq [and gravitational pressure]; Blagojević & Vasilić CQG(02)gq [with cosmological constant]; Maluf et al GRG(07)gq/05 [arbitrary tetrads, background subtraction]; Xu & Jing CQG(06)gq [energy, stationary axisymmetric]; Hermida de La Rica a0905 [conservation]; > s.a. gravitational energy-momentum; gravitational radiation.
@ Other quantities: Maluf et al CQG(06)gq [angular momentum]; Castello-Branco & da Rocha-Neto PRD(12)-a1312 [energy, pressure, thermodynamics].
@ Quantum theory: Mielke PLA(99) [lqg, connection formulation, states constructed from the translational Chern-Simons term]; von Borzeszkowski IJMPA(02); Aldrovandi et al gq/05-conf, AIP(06)gq; Okołów GRG(14)-a1304 [kinematic quantum states], GRG(14)-a1305, GRG(14)-a1308 [variables]; Haro JCAP(13)-a1309 [lqc, cosmological perturbations]; > s.a. regge calculus.

Modified Versions and Related Concepts > s.a. Center of Mass; lattice gravity; Parallelizable Manifold; torsion in physics; unified theories.
* Parametrized: A more general version, in which the curvature does not vanish; Paths can be taken to represent physical trajectories, and is used as basis for a unified theory of gravity and electromagnetism.
@ Teleparallel equivalents for metric theories: Sotiriou et al PRD(11)-a1012 [and local Lorentz invariance].
@ Other teleparallel gravity theories: Müller-Hoissen PRD(83) [two-parameter family of field Lagrangians]; Kofinas & Saridakis PRD(14)-a1404 [Gauss-Bonnet gravity]; Wanas et al G&C(17)-a1404; González & Vásquez PRD(15)-a1508 [Lovelock gravity]; Cai et al RPP(16)-a1511 [f(T) theories and cosmology]; Bahamonde & Böhmer EPJC(16)-a1606 [with Gauss-Bonnet contributions]; Bahamonde et al CQG(19)-a1807 [extended, Noether symmetries and boundary terms]; Itin et al EPJC(18)-a1808 [premetric thory]; González et al JCAP(19)-a1905 [Lovelock gravity]; > s.a. gauge theories of gravity; unimodular relativity.
@ Other teleparallel theories: Maluf & Ulhoa a2010 [massless spin-2 fields].
@ With matter: Mosna & Pereira GRG(04)gq/03 [coupling prescription]; Salti & Aydogdu gq/05-wd [spin-1, Bianchi I models]; Lobo et al a1901-MGXV [theory with non-metricity coupled non-minimally to matter]; Huguet et al PRD(21)-a2008 [coupling to matter with Cartan connection]; > s.a. tachyon fields.
@ Born-Infeld-type modification: Ferraro & Fiorini PRD(07)-gq/06 [and inflation], PRD(08)-a0812 [in Weitzenböck spacetime].
@ Other approaches and variations: Wanas et al ASS(95)gq/02 [path equations]; Itin GRG(99)gq/98, GRG(99)gq/98, IJMPD(01)gq/99 [coframe version]; Nester & Yo ChJP-gq/98 [non-metricity instead of torsion]; de Andrade et al PRD(00) [for Kaluza-Klein theory]; Kohler GRG(00) [semi-teleparallel]; Fonseca IJMPA(02) [and equivalence principle]; Obukhov & Pereira PRD(03) [metric-affine approach]; Maluf & Faria PRD(12)-a1110 [conformally invariant]; Formiga et al PRD(13)-a1302 [Weyl and Weitzenböck spacetimes and the electromagnetic field]; Formiga IJTP(14)-a1401 [extension to Weyl geometry]; Bahamonde et al PRD(15)-a1508; Junior & Rodrigues EPJC(16)-a1509; Ong & Nester EPJC(18)-a1709 [Lagrange multiplier formulation, pathologies]; Beltrán et al PRD(18)-a1710 [symmetric, simpler geometric formulation of general relativity]; Dupuis et al CQG(20)-a1906 [discretization, dual loop gravity].
@ Parametrized: Wanas TJP(00)gq, gq/02-proc, gq/04; Wanas et al G&C(00)gq/98, in(03)gq/05 [spin-gravity interaction, COW results].
@ Cosmology: Hohmann a2011-EPJP [linear perturbations]; > s.a. defects; early-universe nucleosynthesis.
> Other phenomenology: see energy conditions; gravitational radiation; gravitomagnetism.
> Related topics: see metric matching.

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