Teleparallel Structures and Gravity Theories| 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.
main page
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