A Mathematical Journey to Relativity

Boskoff, Wladimir-Georges; Capozziello, Salvatore

doi:10.1007/978-3-030-47894-0

Cited by 12 publications

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“…where the number R * is the curvature scalar of the space submanifold. By rescaling space coordinates, it can be put equal to k = 0, ±1 (see [8]). This equation is independent of the model and of the matter content of the universe, and only descends from the FLRW hypothesis that the spacetime is homogeneous and isotropic.…”

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confidence: 99%

Geometric perfect fluids from Extended Gravity

Capozziello¹,

Mantica²,

Molinari³

2022

EPL

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A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the ﬁeld equations of such theories naturally contain perfect ﬂuid terms. Speciﬁc examples are developed for the Friedman-Lemaˆıtre-Roberson-Walker metric.

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mentioning

confidence: 99%

Geometric perfect fluids from Extended Gravity

Capozziello¹,

Mantica²,

Molinari³

2022

EPL

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Section: Proofmentioning

confidence: 99%

Geometric Perfect Fluids from Extended Gravity

Capozziello,

Mantica,

Molinari

2022

Preprint

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A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the field equations of such theories naturally contain perfect fluid terms. Specific examples are developed for the Friedman-Lemaître-Roberson-Walker metric.

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“…(85), acquires two additional symmetries apart from the antisymmetry in the last two indices. These are given below for ease of reference [65,68] •…”

Section: A Gauss Constraint and Evolution Equations In General Relati...mentioning

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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A Mathematical Journey to Relativity

Cited by 12 publications

References 0 publications

Geometric perfect fluids from Extended Gravity

Geometric perfect fluids from Extended Gravity

Geometric Perfect Fluids from Extended Gravity

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

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