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Showing 1 to 10 of 10 for “"Weyl tensor"”.
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A study of integrability conditions for irrotational dust spacetimes
… dust space times the divergence-free magnetic Weyl tensor and the divergence-free electric Weyl tensor (necessary conditions for gravity waves interacting with matter), both imply integrability conditions in the exact non-linear case. The integrability conditions for the divergence-free …
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Contributions to the study of shear-free and of purely radiative perfect fluids in general relativity
… of the electric and magnetic part of the Weyl tensor.
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Aspects Of The Ricci Flow
… assumption. Finally, we investigate the Weyl tensor within a gradient Ricci soliton struc¨ ture. First, we prove a Bochner-Weitzenbock type formula for the norm of the self-dual Weyl tensor and discuss its applications. We are also concerned with the interplay of curvature components and …
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New approaches to higher-dimensional general relativity
… of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the …
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SPECIAL RIEMANNIAN STRUCTURES ON FOUR-MANIFOLDS: FROM TWISTOR SPACES TO UNOBSTRUCTED CONDITIONS
… characterizations in terms of the Nijenhuis tensors defined on their twistor spaces; moreover, we classify Einstein four-manifolds with positive scalar curvature, under the assumption that the scalar curvature of their twistor spaces is constant on the fibers of the twistor bundle. In the …
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THE COVARIANT APPROACH TO SPACE TIMES ANDSOME EXTENDED THEORIES OF GRAVITY
… Robertson - Walker spacetimes the Ricci tensor is the sum of a perfect fluid term and an anisotropic term given by the electric component of the Weyl tensor. In standard cosmology the anisotropy vanishes: this allows to specify the geometric correction due to the extended theory as a …
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Aspects of higher dimensional Einstein theory and M-theory
… use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is …
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Aspects of modern cosmology
… for the electric and magnetic parts of the Weyl tensor are shown to be of different order. In particular, the electric part appears to have a third order evolution equation, while the magnetic part has a second order evolution equation. It is shown that the "silent" nature of the evolution …
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Topics in relativistic cosmology: Cosmology on the past lightcone and in modified gravitation
… or gravito-electric components of the Weyl tensor vanish. We also discuss the existence and consistency of classes of non-expanding irrotational spacetimes in ƒ(R)-gravity. Furthermore, we explore exact ƒ(R) gravity solutions that mimic Chaplygin-gas inspired ΛCDM cosmology. Starting …
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PERFECT FLUIDS AND SIGMA MODELS: A MATHEMATICAL INVESTIGATION BETWEEN GENERAL RELATIVITY AND COTTON GRAVITY
… on third order derivatives of the metric tensor. In doing so, we will unveil the special relevance that Codazzi tensors hold in this theory, as well as the important relations between the equations of C-φ-PF and the first integrability condition of a φ-SPFST. Inspired by some works in …