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Results 1 - 10
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323
The Weyl Curvature Conjecture
, 2008
"... In this paper we review Penrose’s Weyl curvature conjecture which states that the concept of gravitational entropy and the Weyl tensor is somehow linked, at least in a cosmological setting. We give a description of a certain entity constructed from the Weyl tensor, from the very early history of our ..."
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Cited by 3 (2 self)
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In this paper we review Penrose’s Weyl curvature conjecture which states that the concept of gravitational entropy and the Weyl tensor is somehow linked, at least in a cosmological setting. We give a description of a certain entity constructed from the Weyl tensor, from the very early history
Naked Singularities and the Weyl Curvature Hypothesis
, 1997
"... We examine the growth of the Weyl curvature in two examples of naked singularity formation in spherical gravitational collapse- dust and the Vaidya spacetime. We find that the Weyl scalar diverges along outgoing radial null geodesics as they meet the naked singularity in the past. The implications o ..."
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We examine the growth of the Weyl curvature in two examples of naked singularity formation in spherical gravitational collapse- dust and the Vaidya spacetime. We find that the Weyl scalar diverges along outgoing radial null geodesics as they meet the naked singularity in the past. The implications
WEYL CURVATURE AND THE EULER CHARACTERISTIC IN DIMENSION FOUR
, 2005
"... Abstract. We give lower bounds, in terms of the Euler characteristic, for the L 2-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics. 1. ..."
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Cited by 1 (0 self)
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Abstract. We give lower bounds, in terms of the Euler characteristic, for the L 2-norm of the Weyl curvature of closed Riemannian 4-manifolds. The same bounds were obtained by Gursky, in the case of positive scalar curvature metrics. 1.
Weyl curvature, Einstein metrics, and Seiberg–Witten theory
- Math. Research Letters
, 1998
"... We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates for the L 2-norm of the Weyl curvature of a smooth compact 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics on smooth compact 4-manifolds with a non-zero Seibe ..."
Abstract
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Cited by 10 (1 self)
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We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates for the L 2-norm of the Weyl curvature of a smooth compact 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics on smooth compact 4-manifolds with a non
ON THE SIGNIFICANCE OF THE WEYL CURVATURE IN A RELATIVISTIC COSMOLOGICAL MODEL
, 2009
"... The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of g ..."
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The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions
On cosmological isotropy, quantum cosmology and the weyl curvature hypothesis
- Class. Quantum Grav
, 1993
"... Abstract. The increasing entropy, large-scale isotropy and approximate flatness of the universe are considered in the context of signature change, which is a classical model of quantum tunnelling in quantum cosmology. The signature change hypothesis implies an initial inflationary epoch, the magneti ..."
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Cited by 7 (0 self)
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, the magnetic half of the Weyl curvature hypothesis, and a close analogue of the conformal singularity hypothesis. Adding the electric half of the Weyl curvature hypothesis yields, for a perfect fluid, only homogeneous and isotropic cosmologies. In the cosmological-constant case, the unique solution
The Lanczos potential for the Weyl curvature tensor: existence, wave equation and algorithms
- A
, 1997
"... In the last few years renewed interest in the 3-tensor potential Labc proposed by Lanczos for the Weyl curvature tensor has not only claried and corrected Lanczos’s original work, but generalized the concept in a number of ways. In this paper we rst of all carefully summarize and extend some aspects ..."
Abstract
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Cited by 10 (8 self)
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In the last few years renewed interest in the 3-tensor potential Labc proposed by Lanczos for the Weyl curvature tensor has not only claried and corrected Lanczos’s original work, but generalized the concept in a number of ways. In this paper we rst of all carefully summarize and extend some
The non-existence of a Lanczos potential for the Weyl curvature tensor in dimensions n ≥ 7
, 2002
"... In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension n≥7. ..."
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In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension n≥7.
Results 1 - 10
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323
