Non-Geodesic Incompleteness in Poincaré Gauge Gravity

Cembranos, J. A. R.; Valcárcel, Jorge Gigante; Torralba, Francisco José Maldonado

doi:10.3390/e21030280

Cited by 7 publications

(11 citation statements)

References 29 publications

(43 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Interestingly, these scenarios provide a realisation of the α-attractor model of inflation. 10 We prefer to give the action to make explicit the conformal factors coming from the volume element.…”

mentioning

confidence: 99%

Revisiting the stability of quadratic Poincaré gauge gravity

Jiménez

Torralba

2020

Eur. Phys. J. C

View full text Add to dashboard Cite

show abstract

“…Note that torsion appears in the first three terms, where it has to be replaced by the corresponding matter (spin) quantities via Cartan's Eq. (42). Formally, the tensor U µν obeys the following expression…”

Section: Full Approach Including the Spin Contribution From The Electmentioning

confidence: 99%

Einstein–Cartan–Dirac gravity with U(1) symmetry breaking

Cabral

Rubiera-García

2019

Eur. Phys. J. C

View full text Add to dashboard Cite

Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities. In this work we introduce an extension of the Einstein-Cartan-Dirac theory with an electromagnetic (Maxwell) contribution minimally coupled to torsion. This contribution breaks the U (1) gauge symmetry, which is suggested by the possibility of a torsion-induced phase transition in the early Universe, yielding new physics in extreme (spin) density regimes. We obtain the generalized gravitational, electromagnetic and fermionic field equations for this theory, estimate the strength of the corrections, and discuss the corresponding phenomenology. In particular, we briefly address some astrophysical considerations regarding the relevance of the effects which might take place inside ultra-dense neutron stars with strong magnetic fields (magnetars).

show abstract

“…Consequently attempts to generalise many of the properties and theorems of GR to these torsion theories has been a very active field since the 1980s. Paradigmatic examples include the study of singularities [9][10][11][12], particles motion [13,14] and stability analysis [15][16][17]. The latter reference deserves some attention since in the bulk of this work we shall study the Lagrangian obtained therein, namely the quadratic PG theories fulfilling the following stability conditions on a Minkowski background 1.…”

Section: Introductionmentioning

confidence: 99%

Birkhoff's theorem for stable torsion theories

Cruz-Dombriz

Torralba

2019

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

We present a novel approach to establish the Birkhoff's theorem validity in the so-called quadratic Poincaré Gauge theories of gravity. By obtaining the field equations via the Palatini formalism, we find paradigmatic scenarios where the theorem applies neatly. For more general and physically relevant situations, a suitable decomposition of the torsion tensor also allows us to establish the validity of the theorem. Our analysis shows rigorously how for all stable cases under consideration, the only solution of the vacuum field equations is a torsionless Schwarzschild spacetime, although it is possible to find non-Schwarzschild metrics in the realm of unstable Lagrangians. Finally, we study the weakened formulation of the Birkhoff's theorem where an asymptotically flat metric is assumed, showing that the theorem also holds.1 Not including the traceless tensor part of the torsion in this stability analysis is motivated by the fact that in a cosmological scenario (FRW metric) this component is identically zero. − 16r 2 a(t, r)c(t, r) cos(θ)(cos(2θ) − 3) cot(θ)f (t, r) ψ(t, r) − 16r 2 b(t, r) cos(θ)(cos(2θ) − 3) cot(θ)f (t, r)d(t, r) ψ(t, r) − 8 cos(2θ)f (t, r) 2 sin(θ)l(t, r)φ(t, r) ψ(t, r) + 2 cos(4θ)f (t, r) 2 sin(θ)l(t, r)φ(t, r) ψ(t, r) + 22f (t, r) 2 sin(θ)l(t, r)φ(t, r) ψ(t, r) = 0, (D.16)

show abstract

Non-Geodesic Incompleteness in Poincaré Gauge Gravity

Cited by 7 publications

References 29 publications

Revisiting the stability of quadratic Poincaré gauge gravity

Revisiting the stability of quadratic Poincaré gauge gravity

Einstein–Cartan–Dirac gravity with U(1) symmetry breaking

Birkhoff's theorem for stable torsion theories

Contact Info

Product

Resources

About