Vacuum static spaces with vanishing of complete divergence of Weyl tensor

DOI10.1007/s12220-020-00384-4zbMath1477.53096arXiv1812.11744OpenAlexW3014468505MaRDI QIDQ2659527

Gabjin Yun, Seungsu Hwang

Publication date: 26 March 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11744

zbMATH Keywords

black holesWeyl tensorEinstein metricvacuum static spaceBach tensorBesse conjecture

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Critical metrics (58E11)

Related Items (7)

Besse conjecture with positive isotropic curvature ⋮ Certain almost Kenmotsu metrics satisfying the vacuum static equation ⋮ On the geometry of electrovacuum spaces in higher dimensions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Vanishing conditions on Weyl tensor for Einstein-type manifolds ⋮ Closed vacuum static spaces with zero radial Weyl curvature

Cites Work

• Unnamed Item
• Unnamed Item
• A note on static spaces and related problems
• Total scalar curvature and harmonic curvature
• Nonexistence of multiple black holes in static space-times and weakly harmonic curvature
• Sur la géométrie d'une généralisation de l'équation différentielle d'Obata
• A negative answer to a conjecture of conformal transformations of Riemannian manifolds
• A differential equation arising from scalar curvature function
• Four-dimensional static and related critical spaces with harmonic curvature
• On Bach-flat gradient shrinking Ricci solitons
• Scalar curvature, metric degenerations and the static vacuum Einstein equations on 3-manifolds. I
• Rigidity of gradient Ricci solitons
• Gradient Ricci solitons with vanishing conditions on Weyl
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• A note on Fischer-Marsden’s conjecture
• Manifolds of Riemannian metrics with prescribed scalar curvature
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations

This page was built for publication: Vacuum static spaces with vanishing of complete divergence of Weyl tensor