Modified teleparallel theories of gravity in symmetric spacetimes - INSPIRE

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Modified teleparallel theories of gravity in symmetric spacetimes

Manuel Hohmann
(
- Tartu U.
)
,
Laur Järv
(
- Tartu U.
)
,
Martin Krššák
(
- Yangzhou U. and
- Tartu U.
)
,
Christian Pfeifer
(
- Tartu U.
)

Jan 16, 2019

23 pages

Published in:

Phys.Rev.D 100 (2019) 8, 084002

Published: Oct 2, 2019

e-Print:

1901.05472 [gr-qc]

DOI:

10.1103/PhysRevD.100.084002 (publication)

View in:

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Abstract: (APS)

Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain amounts of symmetry, such as spherical or cosmological symmetry. In this article we present how to apply the notion of spacetime symmetries known from Cartan geometry to teleparallel geometries. We explicitly derive the most general tetrads and spin connections which are compatible with axial, spherical, cosmological, and maximal symmetry. For homogeneous and isotropic spacetime symmetry we find that the tetrads and spin connection found by the symmetry constraints are universal solutions to the antisymmetric part of the field equations of any teleparallel theory of gravity. In other words, for cosmological symmetry we find what has become known as “good tetrads” in the context of f(T) gravity.

Note:

27 pages, no figures; final version accepted by Physical Review D

General relativity, alternative theories of gravity
symmetry: space-time
gravitation: teleparallel
space-time: teleparallel
geometry: teleparallel
geometry: Cartan
tetrad
field equations: solution
spin
covariance

References(52)

Figures(0)

[1]

f(R) theories

- Living Rev.Rel. 13 (2010) 3
•
e-Print:
- 1002.4928
•
DOI:
- 10.12942/lrr-2010-3

[2]

Extended Theories of Gravity

Salvatore Capozziello
(
- INFN, Naples and
- Naples U.
)
,
Mariafelicia De Laurentis
(
- INFN, Naples and
- Naples U.
)

- Phys.Rept. 509 (2011) 167-321
•
e-Print:
- 1108.6266
•
DOI:
- 10.1016/j.physrep.2011.09.003

[3]

Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

S. Nojiri
(
- KMI, Nagoya and
- Nagoya U.
)
,
S.D. Odintsov
(
- Barcelona, IEEC and
- ICREA, Barcelona
)
,
V.K. Oikonomou
(
- Tomsk Pedagogical Inst. and
- TUSUR, Tomsk
)

- Phys.Rept. 692 (2017) 1-104
•
e-Print:
- 1705.11098
•
DOI:
- 10.1016/j.physrep.2017.06.001

[4]

Albert Einstein: Akademie‐Vorträge: Sitzungsberichte der Preußischen Akademie der Wissenschaften 1914–1932

A. Einstein

[5]

Field equations in teleparallel spacetime: Einstein's fernparallelismus approach towards unified field theory

Tilman Sauer
(
- Caltech
)

- Historia Math. 33 (2006) 399-439
•
e-Print:
- physics/0405142
•
DOI:
- 10.1016/j.hm.2005.11.005

[6]

C. Møller

- Kong.Dan.Vid.Sel.Mat.Fys.Med. 1 (1961) 1

[7]

Extended translation invariance and associated gauge fields

K. Hayashi
(
- Kyoto U.
)
,
T. Nakano
(
- Osaka City U.
)

- Prog.Theor.Phys. 38 (1967) 491-507,
•
DOI:
- 10.1143/PTP.38.491

[8]

Einstein Lagrangian as the Translational Yang-Mills Lagrangian

Y.M. Cho
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Rev.D 14 (1976) 2521,
•
DOI:
- 10.1103/PhysRevD.14.2521

[9]

The Gauge Theory of the Translation Group and Underlying Geometry

Kenji Hayashi
(
- Munich, Max Planck Inst.
)

- Phys.Lett.B 69 (1977) 441-444
•
DOI:
- 10.1016/0370-2693(77)90840-1

[10]

Teleparallel Gravity

R. Aldrovandi
,
J.G. Pereira

[11]

Teleparallel theories of gravity: illuminating a fully invariant approach

M. Krssak
(
- Tartu U. and
- Yangzhou U.
)
,
R.J. van den Hoogen
(
- St. Francis Xavier U.
)
,
J.G. Pereira
(
- Sao Paulo, IFT
)
,
C.G. Böhmer
(
- U. Coll. London
)
,
A.A. Coley
(
- Dalhousie U., Math. Dept.
)

- Class.Quant.Grav. 36 (2019) 18, 183001
•
e-Print:
- 1810.12932
•
DOI:
- 10.1088/1361-6382/ab2e1f

[12]

Modified teleparallel gravity: Inflation without inflaton

Rafael Ferraro
(
- Buenos Aires, IAFE and
- Buenos Aires U.
)
,
Franco Fiorini
(
- Buenos Aires, IAFE
)

- Phys.Rev.D 75 (2007) 084031
•
e-Print:
- gr-qc/0610067
•
DOI:
- 10.1103/PhysRevD.75.084031

[13]

Dark torsion as the cosmic speed-up

Gabriel R. Bengochea
(
- Buenos Aires, IAFE and
- Buenos Aires U.
)
,
Rafael Ferraro
(
- Buenos Aires, IAFE and
- Buenos Aires U.
)

- Phys.Rev.D 79 (2009) 124019
•
e-Print:
- 0812.1205
•
DOI:
- 10.1103/PhysRevD.79.124019

[14]

On Born-Infeld Gravity in Weitzenbock spacetime

Rafael Ferraro
(
- Buenos Aires, IAFE and
- Buenos Aires U.
)
,
Franco Fiorini
(
- Buenos Aires, IAFE
)

- Phys.Rev.D 78 (2008) 124019
•
e-Print:
- 0812.1981
•
DOI:
- 10.1103/PhysRevD.78.124019

[15]

Einstein's Other Gravity and the Acceleration of the Universe

Eric V. Linder
(
- UC, Berkeley and
- Ewha Women's U., Seoul
)

- Phys.Rev.D 81 (2010) 127301,
- Phys.Rev.D 82 (2010) 109902 (erratum)
•
e-Print:
- 1005.3039
•
DOI:
- 10.1103/PhysRevD.81.127301

[15]

Einstein's Other Gravity and the Acceleration of the Universe

Eric V. Linder
(
- UC, Berkeley and
- Ewha Women's U., Seoul
)

- Phys.Rev.D 81 (2010) 127301,
- Phys.Rev.D 82 (2010) 109902 (erratum)
•
e-Print:
- 1005.3039
•
DOI:
- 10.1103/PhysRevD.81.127301

[16]

f(T) teleparallel gravity and cosmology

Yi-Fu Cai
(
- CUST, SKLPDE and
- Hefei, CUST and
- McGill U.
)
,
Salvatore Capozziello
(
- Frankfurt U. and
- Tomsk Pedagogical Inst. and
- Tomsk State U. and
- INFN, Naples
)
,
Mariafelicia De Laurentis
(
- Frankfurt U. and
- INFN, Naples and
- Naples U.
)
,
Emmanuel N. Saridakis
(
- Valparaiso U., Catolica and
- Baylor U. and
- Natl. Tech. U., Athens
)

- Rept.Prog.Phys. 79 (2016) 10, 106901
•
e-Print:
- 1511.07586
•
DOI:
- 10.1088/0034-4885/79/10/106901

[17]

$f(T)$ gravity and local Lorentz invariance

Baojiu Li
(
- Cambridge U., DAMTP and
- Cambridge U., KICC
)
,
Thomas P. Sotiriou
(
- Cambridge U., DAMTP
)
,
John D. Barrow
(
- Cambridge U., DAMTP
)

- Phys.Rev.D 83 (2011) 064035
•
e-Print:
- 1010.1041
•
DOI:
- 10.1103/PhysRevD.83.064035

[18]

Generalizations of teleparallel gravity and local Lorentz symmetry

Thomas P. Sotiriou
(
- Cambridge U., DAMTP
)
,
Baojiu Li
(
- Cambridge U., DAMTP and
- Cambridge U.
)
,
John D. Barrow
(
- Cambridge U., DAMTP
)

- Phys.Rev.D 83 (2011) 104030
•
e-Print:
- 1012.4039
•
DOI:
- 10.1103/PhysRevD.83.104030

[19]

Non trivial frames for f(T) theories of gravity and beyond

Rafael Ferraro
(
- Buenos Aires, IAFE and
- Buenos Aires U.
)
,
Franco Fiorini
(
- Buenos Aires, IAFE
)

- Phys.Lett.B 702 (2011) 75-80
•
e-Print:
- 1103.0824
•
DOI:
- 10.1016/j.physletb.2011.06.049

[20]

Good and bad tetrads in f(T) gravity

- Phys.Rev.D 86 (2012) 044009
•
e-Print:
- 1204.4593
•
DOI:
- 10.1103/PhysRevD.86.044009

[21]

The covariant formulation of f(T) gravity

Martin Krššák
(
- Sao Paulo, IFT
)
,
Emmanuel N. Saridakis
(
- Baylor U. and
- Valparaiso U., Catolica
)

- Class.Quant.Grav. 33 (2016) 11, 115009
•
e-Print:
- 1510.08432
•
DOI:
- 10.1088/0264-9381/33/11/115009

[22]

Covariant formulation of scalar-torsion gravity

Manuel Hohmann
(
- Tartu, Inst. Phys.
)
,
Laur Järv
(
- Tartu, Inst. Phys.
)
,
Ulbossyn Ualikhanova
(
- Tartu, Inst. Phys.
)

- Phys.Rev.D 97 (2018) 10, 104011
•
e-Print:
- 1801.05786
•
DOI:
- 10.1103/PhysRevD.97.104011

[23]

Metric affine approach to teleparallel gravity

Yu.N. Obukhov
(
- Sao Paulo, IFT
)
,
J.G. Pereira
(
- Sao Paulo, IFT
)

- Phys.Rev.D 67 (2003) 044016
•
e-Print:
- gr-qc/0212080
•
DOI:
- 10.1103/PhysRevD.67.044016

[24]

Covariance properties and regularization of conserved currents in tetrad gravity

Yuri N. Obukhov
(
- Sao Paulo, IFT and
- Moscow State U.
)
,
Guillermo F. Rubilar
(
- Sao Paulo, IFT and
- Concepcion U.
)

- Phys.Rev.D 73 (2006) 124017
•
e-Print:
- gr-qc/0605045
•
DOI:
- 10.1103/PhysRevD.73.124017

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