Exploring axial symmetry in modified teleparallel gravity

Bahamonde, Sebastián; Valcárcel, Jorge Gigante; Järv, Laur; Pfeifer, Christian

doi:10.1103/physrevd.103.044058

Cited by 35 publications

(41 citation statements)

References 87 publications

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“…To obtain the influence of the teleparallel perturbation on a realistic black hole shadow the whole derivation has to be extended to rotating axially symmetric black holes. The derivation of teleparallel perturbations of Kerr spacetime is currently work in progress, and first steps towards this goal have been achieved [51].…”

Section: Discussionmentioning

confidence: 99%

“…The Lorentz matrices are pure gauge fields and, without loss of generality, it is possible to work in the so called Weitzenböck gauge, in which one absorbs the Lorentz matrices in the tetrad. As a consequence one can globally work with zero spin connection in this gauge, see, for example, ( [51] (Eq. (4))) for a detailed derivation.…”

Section: Covariant F (T) Gravitymentioning

confidence: 99%

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Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Pfeifer

Schuster

2021

Universe

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With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.

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Section: Discussionmentioning

confidence: 99%

Section: Covariant F (T) Gravitymentioning

confidence: 99%

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Pfeifer

Schuster

2021

Universe

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“…While in the teleparallel equivalent of Einstein gravity, the field equations do not determine the spin connection (and one can thus use the approach of [10] to fix it by demanding that in the absence of gravity flat space is a solution), this is no longer true for f (T ) gravity and other generalisations. It appears that solving for a suitable spin connection is a non-trivial problem in that case in general, even if one assumes a highly symmetric geometry [15,39,40]. In the Kerr-Schild ansatz we have presented, this difficulty is fortunately absent for a flat background spacetime, but it needs to be checked whether that remains true in the case where also the background is curved.…”

Section: Discussionmentioning

confidence: 95%

“…Furthermore, it would be interesting to also generalise the Kerr-Schild ansatz to symmetric teleparallel gravity [41,42], where both curvature and torsion vanish and gravitation is described by non-metricity, and to find mappings between those different descriptions. Another venue of generalisation would include more general actions that not only involve the torsion scalar, but also matter fields such as in [40] where a scalar field with quite arbitrary kinetic term and potential was studied. It should be possible to find solutions at least in simple cases, for example including electromagnetic fields where the solution is known in Einstein gravity [4]; in the general case, the results of [43] might be helpful.…”

Section: Discussionmentioning

confidence: 99%

Kerr–Schild metrics in teleparallel gravity

Fröb

2021

Eur. Phys. J. C

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We show that the Kerr–Schild ansatz can be extended from the metric to the tetrad, and then to teleparallel gravity where curvature vanishes but torsion does not. We derive the equations of motion for the Kerr–Schild null vector, and describe the solution for a rotating black hole in this framework. It is shown that the solution depends on the chosen tetrad in a non-trivial way if the spin connection is fixed to be the one of the flat background spacetime. We show furthermore that any Kerr–Schild solution with a flat background is also a solution of $$f({\mathcal {T}})$$ f ( T ) gravity.

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“…This assumption that one could objectively separate gravity from inertia goes against all experimental evidence, And it is related to the picture of (fictional) global translations being gauged, and requires some, necessarily voluntary, choice of the reference tetrad. By now, it is known that the standard recipes [19] of determining the spin connection can give non-unique results [33], and beyond the simplest cases they might even easily get wrong, with equations of motion not being satisfied if not in TEGR [34].…”

Section: Lorentz Gauge-invariant Variablesmentioning

confidence: 99%

Lorentz gauge-invariant variables in torsion-based theories of gravity

Blixt,

Ferraro,

Golovnev

et al. 2022

Preprint

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General relativity dynamics can be derived from different actions -which depart from the Einstein-Hilbert action in boundary terms-and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general relativity is a torsion-based theory for the tetrad field. More general torsion-based theories have been built in the last years, intending to supersede general relativity. There are two current ways to formulate such theories; one includes a spin-connection and the other does not. We discuss the notion of Lorentz gauge invariance in such theories, and give a simple but important proof that both formulations are physically equivalent.

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Exploring axial symmetry in modified teleparallel gravity

Cited by 35 publications

References 87 publications

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

Kerr–Schild metrics in teleparallel gravity

Lorentz gauge-invariant variables in torsion-based theories of gravity

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