xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

Hohmann, Manuel

doi:10.1140/epjc/s10052-021-09183-9

Cited by 8 publications

(7 citation statements)

References 54 publications

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“…while the remaining parameters vanish again, indicating that the theory is fully conservative, i.e., there are no preferred-frame or preferred-location effects or violation of total energy-momentum conservation. Taking a closer look at this result, one finds that even in this class there is another subclass given by l Y = 0 corresponding to a minimally coupled scalar field at the linear perturbation order which leads to the general relativity values (39). Further, we find that for 4l 2 Y + l X l Q = 0 the PPN parameters β and γ diverge.…”

Section: Ppn Parametersmentioning

confidence: 64%

“…Potential deviations from these values are encountered only in the subclass l Y + l Z = 0. Within this subclass, we found that theories which in addition satisfy l X = l Y = 0, so that the scalar field is minimally coupled to nonmetricity at the linear order, again yield the same PPN parameters (39). For theories with 3l 2 Y + l X l Q = 0 we obtain the PPN parameters…”

Section: Ppn Parametersmentioning

confidence: 75%

“…We proceed in ascending velocity orders; the zeroth, second, third and fourth velocity order is discussed in sections IV A, IV B, IV C and IV D, respectively. Calculations have been performed using xPPN [39]. Alternatively, one could make use of the gauge-invariant approach to the PPN formalism [36,40]; the resulting equations for the constant coefficients we obtain are identical.…”

Section: Solving the Field Equationsmentioning

confidence: 99%

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Post-Newtonian limit of generalized scalar-torsion theories of gravity

Flathmann

Hohmann

2020

Phys. Rev. D

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In this article we derive the post-Newtonian limit of a class of teleparallel theories of gravity, where the action is a free function L(T, X, Y, φ) of the Torsion scalar T and scalar quantities X and Y built from the dynamical scalar field φ. We restrict the analysis to a massless scalar field in order to use the parameterized post-Newtonian formalism without modifications, such as introducing an effective gravitational constant which depends on the distance between the interacting masses. In particular the results show a class of fully-conservative theories of gravity, where the only nonvanishing parameters are γ and β. For a particular choice of the function L(T, X, Y, φ) the theory cannot be distinguished from General Relativity in its post-Newtonian approximation.

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Section: Ppn Parametersmentioning

confidence: 64%

Section: Ppn Parametersmentioning

confidence: 75%

Section: Solving the Field Equationsmentioning

confidence: 99%

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Post-Newtonian limit of generalized scalar-torsion theories of gravity

Flathmann

Hohmann

2020

Phys. Rev. D

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“…In this article we will follow [77] by using the following syntax highlighting for code listings: keywords for Mathematica are typeset in green, for xAct in blue and for HiGGS in red. This paper uses the 'West coast' signature (+, −, −, −).…”

Section: A Conventionsmentioning

confidence: 99%

Supercomputers against strong coupling in gravity with curvature and torsion

Barker¹

2022

Preprint

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Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. These non-Riemannian or Poincaré gauge theories suffer notoriously from strong coupling. The implementation forms a package (the 'Hamiltonian Gauge Gravity Surveyor' -HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets can be evaluated in parallel, meaning that Hamiltonian analysis can be done on silicon, and at scale. Accordingly HiGGS is designed to survey the whole Lagrangian space with high-performance computing resources (clusters and supercomputers). To demonstrate this, the space of 'outlawed' Poincaré gauge theories is surveyed, in which a massive parity-even/odd vector or parity-odd tensor torsion particle accompanies the usual graviton. The survey spans possible configurations of teleparallel-style multiplier fields which might be used to kill-off the strongly coupled modes, with the results to be analysed in subsequent work. All brackets between the known primary and secondary constraints of all theories are made available for future study. Demonstrations are also given for using HiGGS -on a desktop computer -to run the Dirac-Bergmann algorithm on specific theories, such as Einstein-Cartan theory and its minimal extensions.

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“…For instance, in TG, Refs. [32][33][34][35] have explored important parts of the decomposition of TEGR. On the other end of the spectrum, Refs.…”

Section: Introductionmentioning

confidence: 99%

The $3+1$ Formalism in the Geometric Trinity of Gravity

Capozziello,

Finch,

Said

et al. 2021

Preprint

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The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a 3 + 1 decomposition of the teleparallel equivalent of general relativity and the symmetric teleparallel equivalent of general relativity which are both dynamically equivalent to curvature based general relativity. By splitting the spacetime metric and corresponding tetrad into their spatial and temporal parts as well as through finding the Gauss-like equations, it is possible to set up a general foundation for the different formulations of gravity. Based on these results, general 3-tetrad and 3-metric evolution equations are derived. Finally through the choice of the two respective connections, the metric 3 + 1 formulation for general relativity is recovered as well as the tetrad 3 + 1 formulation of the teleparallel equivalent of general relativity and the metric 3 + 1 formulation of symmetric teleparallel equivalent of general relativity. The approach is capable, in principle, of resolving common features of the various formulations of general relativity at a fundamental level and pointing out characteristics that extensions and alternatives to the various formulations can present.

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xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

Cited by 8 publications

References 54 publications

Post-Newtonian limit of generalized scalar-torsion theories of gravity

Post-Newtonian limit of generalized scalar-torsion theories of gravity

Supercomputers against strong coupling in gravity with curvature and torsion

The $3+1$ Formalism in the Geometric Trinity of Gravity

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