Birkhoff's theorem for stable torsion theories

Cruz-Dombriz, Álvaro de la; Torralba, Francisco José Maldonado

doi:10.1088/1475-7516/2019/03/002

Cited by 16 publications

(10 citation statements)

References 75 publications

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“…This mixing between the field strengths of the trace and axial components cannot stabilise the ghost-like instability of the parity preserving theory for any choice of κ . The kinetic matrix adding the parity violating term to (14) iŝ…”

Section: Parity-violating Termsmentioning

confidence: 99%

“…Since the inception of the Poincaré Gauge Theories (PGTs), the different attempts to generalise the properties and theorems of General Relativity (GR) have been a very active field. Paradigmatic examples include the study of singularities [7][8][9][10][11], the Birkhoff theorem [12][13][14], existence of exact solutions [15][16][17][18][19][20], cosmology [21][22][23][24][25][26], the motion of particles [27,28] and stability analysis [29][30][31][32][33][34][35]. Unveiling the fields content along with their stable/unstable nature is of course one of the most important questions for the viability of the theories with a crucial impact on the reliability of their phenomenology.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Revisiting the stability of quadratic Poincaré gauge gravity

Jiménez

Torralba

2020

Eur. Phys. J. C

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Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence of these pathological couplings results in a theory where either the axial sector or the torsion trace becomes a ghost. We conclude that imposing ghost-freedom generically leads to a non-dynamical torsion. We analyse however two special choices of parameters that allow a dynamical scalar in the torsion and obtain the corresponding effective action where the dynamics of the scalar is apparent. These special cases are shown to be equivalent to a generalised Brans–Dicke theory and a Holst Lagrangian with a dynamical Barbero–Immirzi pseudoscalar field respectively. The two sectors can co-exist giving a bi-scalar theory. Finally, we discuss how the ghost nature of the vector sector can be avoided by including additional dimension four operators.

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Section: Parity-violating Termsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Revisiting the stability of quadratic Poincaré gauge gravity

Jiménez

Torralba

2020

Eur. Phys. J. C

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“…In the strong version, the spherical symmetry is understood as the form-invariance of physical and geometrical variables under the SO(3) group of rotations, whereas in the weak O(3) version one assumes the invariance under the rotations and spatial reflections. The earlier work was confined to the parity-even Lagrangians only [34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Generalized Birkhoff theorem in the Poincaré gauge gravity theory

Obukhov

2020

Preprint

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The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincaré gauge gravity theory. The class of models with the most general Lagrangians of the Yang-Mills type constructed from all possible quadratic invariants of the curvature and the torsion is considered, including both parity-even and parity-odd sectors. We find the models in which the weak and strong versions of the generalized Birkhoff theorem are valid, by making use of the double duality technique.

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“…In the case of stable local Poincaré Gauge theories of gravity, in the limit M s → ∞, the singularity at r = R is unavoidable, see [22]. Within the infinite derivative theory of Poincaré gravity, which has no ghosts, the ring singularity can be smeared out.…”

mentioning

confidence: 99%