The quadratic symmetric teleparallel gravity in two dimensions

Adak, Muzaffer; Dereli, Tekin

doi:10.1209/0295-5075/82/30008

Cited by 11 publications

(8 citation statements)

References 10 publications

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“…On the other hand, one could also use the standard TEGR way of dealing with spinors in the STG, that is, replace the Levi-Civita connection into the equation of motion for the spinors, rewritten in terms of non-metricity, i.e. employ a connection Γ α µν = −L α µν (such a prescription was deduced for the parallel transport of vectors in STG [89]), then arriving at the Dirac equation in the from presented in ref. [52].…”

Section: Jcap08(2018)039mentioning

confidence: 99%

Teleparallel Palatini theories

Jiménez

Heisenberg

Koivisto

2018

J. Cosmol. Astropart. Phys.

173

115

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The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.

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Section: Jcap08(2018)039mentioning

confidence: 99%

Teleparallel Palatini theories

Jiménez

Heisenberg

Koivisto

2018

J. Cosmol. Astropart. Phys.

173

115

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“…Indeed, this correction arises in many versions of string theory [9] and in loop quantum gravity [10][11][12]. Furthermore, CS gravity can be recovered as a truncation of low energy effective string models [8,13] and could also explain several problems in cosmology [14][15][16][17][18] (see Ref. [19] for a recent review).…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves from extreme mass-ratio inspirals in dynamical Chern-Simons gravity

2011

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Dynamical Chern-Simons gravity is an interesting extension of general relativity, which finds its way in many different contexts, including string theory, cosmological settings, and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasicircular inspiralling of a small, stellar-mass object into a large nonrotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green's function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively

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“…1. If we start with the Minkowski spacetime in the cartesian coordinates in which case Q µν = 0, T µ = 0, R µ ν = 0, after a Weyl transformation they become Q µν = −g µν e 2ψ(x) dψ(x) = 0, T µ = 0, R µ ν = 0 which is called the symmetric teleparallel (or Minkowski-Weyl) geometry [10].…”

Section: A Local General Coordinate Transformation Weyl Transformatio...mentioning

confidence: 99%

Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity

Pala¹,

Sert²,

Adak³

2022

Preprint

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We give a new prescription of parallel transport of a vector tangent to a curve which is invariant under both of a local general coordinate and a Weyl transformations. Thus since the length of tangent vector does not change during parallel transport along a closed curve in spacetimes with non-metricity, a second clock effect does not appear in general, not only for the inetgrable Weyl spacetime. We have specially motivated the problem from the point of view of symmetric teleparallel (or Minkowski-Weyl) geometry. We also conclude that as long as nature respects Lorentz symmetry and Weyl symmetry, one can only develop alternative gravity models in the symmetric teleparallel spacetime (Q = 0, T = R = 0) or the most general non-Riemannian spacetime

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The quadratic symmetric teleparallel gravity in two dimensions

Cited by 11 publications

References 10 publications

Teleparallel Palatini theories

Teleparallel Palatini theories

Gravitational waves from extreme mass-ratio inspirals in dynamical Chern-Simons gravity

Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity

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