Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions

Golovnev, Alexey

doi:10.1088/1361-6382/ac2136

Cited by 29 publications

(26 citation statements)

References 37 publications

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“…What is shown in the literature is impossibility of diagonal spherically symmetric tetrads in the standard spherical coordinates. At the same time, one can show that diagonal tetrads in Cartesian coordinates are possible for this metric [37]. They are related to the usual non-diagonal tetrads used in most of the current literature on this topic via the corresponding coordinate transformations.…”

Section: The Current Situation With Black Hole Solutionsmentioning

confidence: 73%

Revisiting diagonal tetrads: new Black Hole solutions in f(T) gravity

et al. 2022

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We study various forms of diagonal tetrads that accommodate Black Hole solutions in f(T) gravity with certain symmetries. As is well-known, vacuum spherically symmetric diagonal tetrads lead to rather boring cases of constant torsion scalars. We extend this statement to other possible horizon topologies, namely, spherical, hyperbolic and planar horizons. All such cases are forced to have constant torsion scalars to satisfy the anti-symmetric part of the field equations. We give a full classification of possible vacuum static solutions of this sort. Furthermore, we discuss addition of time-dependence in all the above cases. We also show that if all the components of a diagonal tetrad depend only on one coordinate, then the anti-symmetric part of the field equations is automatically satisfied. This result applies to the flat horizon case with Cartesian coordinates. For solutions with a planar symmetry (or a flat horizon), one can naturally use Cartesian coordinates on the horizon. In this case, we show that the presence of matter is required for existence of non-trivial solutions. This is a novel and very interesting feature of these constructions. We present two new exact solutions, the first is a magnetic Black Hole which is the magnetic dual of a known electrically charged Black Hole in literature. The second is a dyonic Black Hole with electric and magnetic charges. We present some features of these Black holes, namely, extremality conditions, mass, behavior of torsion and curvature scalars near the singularity.

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Section: The Current Situation With Black Hole Solutionsmentioning

confidence: 73%

Revisiting diagonal tetrads: new Black Hole solutions in f(T) gravity

et al. 2022

Self Cite

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show abstract

“…We term the vanishing of covariant divergence of the left hand side of any modified gravity theories, the extended Bianchi identity. This issue is also present in the f(T) theories [22][23][24][25][26][27][28][29][30][31][32], and we observe that the anti-symmetric part of the field equation of f(T) obtained from the variation of the action term with respect to the metric tensor actually equals the field equation obtained from the variation of the same action by the affine connection. So only when the connection's field equation in f(T) is fulfilled by some model in some underlying geometry, the anti-symmetric part of the metric field equation vanishes and it in turn confirms that the energy conservation is satisfied by that f(T) model.…”

Section: Introductionmentioning

confidence: 69%

On the viability of f(Q) gravity models

Loo

2023

Class. Quantum Grav.

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In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in $f(R)$ theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally $f(Q)$ model specific. We further prove that the energy conservation criterion is equivalent to the affine connection's field equation of $f(Q)$ theory, and except the $f(Q)=\alpha Q+\beta$ model, the non-linear $f(Q)$ models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless $Q$ itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support.

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“…What is shown in the literature is impossibility of diagonal spherically symmetric tetrads in the standard spherical coordinates. At the same time, one can show that a diagonal tetrad in Cartesian coordinates is possible for this metric [37]. They are related to the usual non-diagonal tetrads used in most of the current literature on this topic via the corresponding coordinate transformations.…”

Section: The Current Situation With Black Hole Solutionsmentioning

confidence: 77%

Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity

Awad¹,

Golovnev²,

Guzmán³

et al. 2022

Preprint

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We study various forms of diagonal tetrads that accommodate Black Hole solutions in f (T ) gravity with certain symmetries. As is well-known, vacuum spherically symmetric diagonal tetrads lead to rather boring cases of constant torsion scalars. We extend this statement to other possible horizon topologies, namely, spherical, hyperbolic and planar horizons. All such cases are forced to have constant torsion scalars to satisfy the antisymmetric part of the field equations. We give a full classification of possible vacuum static solutions of this sort. Furthermore, we discuss addition of time-dependence in all the above cases. We also show that if all the components of a diagonal tetrad depend only on one coordinate, then the anti-symmetric part of the field equations is automatically satisfied. This result applies to the flat horizon case with Cartesian coordinates. For solutions with a planar symmetry (or a flat horizon), one can naturally use Cartesian coordinates on the horizon. In this case, we show that the presence of matter is required for existence of non-trivial solutions. This is a novel and very interesting feature of these constructions. We present two new exact solutions, the first is a magnetic Black Hole which is the magnetic dual of a known electrically charged Black Hole in literature. The second is a dyonic Black Hole with electric and magnetic charges. We present some features of these Black holes, namely, extremality conditions, mass, behavior of torsion and curvature scalars near the singularity.

show abstract

Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions

Cited by 29 publications

References 37 publications

Revisiting diagonal tetrads: new Black Hole solutions in f(T) gravity

Revisiting diagonal tetrads: new Black Hole solutions in f(T) gravity

On the viability of f(Q) gravity models

Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity

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