Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

Järv, Laur; Hohmann, Manuel; Krššák, Martin; Pfeifer, Christian

doi:10.3390/universe5060142

Cited by 26 publications

(31 citation statements)

References 73 publications

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“…The tetrad has 16 components: 10 describe the spacetime metric, and 6 correspond to the choice of frame in tangent space. The information about the choice of frame is also carried by the spin connection, so there are 6 redundant gauge degrees of freedom: we can specify the frame using either the tetrad or the spin connection [8,115,123,169,170].…”

Section: Affine Connection and Spin Connectionmentioning

confidence: 99%

Higgs inflation and teleparallel gravity

Raatikainen

Räsänen

2019

J. Cosmol. Astropart. Phys.

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Teleparallel gravity is a formulation of general relativity that is physically equivalent to metric gravity if the gravitational action has the Einstein-Hilbert form and matter is minimally coupled. However, scalar fields generally couple directly to the connection, breaking the equivalence. In particular, this happens for the Standard Model Higgs. We show that a teleparallel theory with a non-minimally coupled scalar field has no linear scalar perturbations, and therefore cannot give successful inflation, unless the non-minimal coupling functions satisfy a particular relation. If the relation is satisfied, Higgs inflation can give an arbitrarily large tensor-to-scalar ratio r. Our results also apply to f (T ) theories, as they are scalar-tensor theories written in different field coordinates. We discuss generalisation to more complicated actions.

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Section: Affine Connection and Spin Connectionmentioning

confidence: 99%

Higgs inflation and teleparallel gravity

Raatikainen

Räsänen

2019

J. Cosmol. Astropart. Phys.

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“…There are various approaches to determining these preferred tetrads, or alternatively the corresponding spin connections [30,36,38,39]. We have considered here the approach of "switching-off" gravity introduced in [17] and further developed in [22][23][24][25]29].…”

Section: Discussionmentioning

confidence: 99%

On conserved quantities for the Schwarzschild black hole in teleparallel gravity

et al. 2021

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We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $$\xi $$ ξ and we consider two different options where $$\xi $$ ξ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine an inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the “switching-off” gravity method where different tetrads can share the same inertial spin connection.

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“…Although one might object that the violation of Diffeomorphisms is caused precisely by our choice of coordinates, we should remember that the connection actually plays the role of Diff-Stückelbergs, and this should now be apparent from the action (13). In fact, the singular property of the STEGR is that even in this gauge, Diffeomorphisms invariance arises as a gauge symmetry of the theory.…”

Section: Framing Symmetric Teleparallelismsmentioning

confidence: 98%

“…However, most of these studies, including the one at hand, focus on non-linear modifications of the teleparallel equivalents of GR (which, from the perspective of teleparallelism as the low-energy manifestation of the ultra-massive spacetime connection, could perhaps be interpreted as non-linear extensions of the quadratic Proca-like term) which have been mainly motivated by their potential use as models of cosmological inflation and dark energy (and even dark matter [6,7]). The non-linear extension of TEGR, the f (T) theory [8], has been considered in, e.g., [9][10][11][12][13][14][15][16][17][18], and the non-linear extension of STEGR, the f (Q) [4] and related theories have been considered in, e.g., [19][20][21][22][23][24][25][26][27][28]. The general teleparallel equivalent of GR, not subject to either the metric or the symmetric condition, was introduced quite recently [29], and only in this paper do we take some first steps towards understanding the properties of the non-linearly extended f (G) theory.…”

Section: Introductionmentioning

confidence: 99%

“…The theory in this gauge defines the STEGR or Coincident GR (alluding to the gauge choice) and is described by the non-metricity scalar Q =G(T α µν = 0). Non-linear extensions based on the above two gauge choices [4,8] have been considered in the literature at some length [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Regarding these generalisations, it is important to notice that the presence of the different boundary terms is what makes the non-linear extensions based on different gauge choices give rise to different theories.…”

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confidence: 99%

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Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Jiménez

Koivisto

2021

Universe

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In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

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Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

Cited by 26 publications

References 73 publications

Higgs inflation and teleparallel gravity

Higgs inflation and teleparallel gravity

On conserved quantities for the Schwarzschild black hole in teleparallel gravity

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

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