Kähler metrics via Lorentzian Geometry in dimension four

Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under c...

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Autores principales:	Aazami Amir Babak, Maschler Gideon
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	kahler metric lorentzian metric shear twist integrable complex structures warped products de sitter spacetime kerr metric gravitational waves pp waves petrov type 53b30 53b55 53c55 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/42169163a00e455f87d68247a1a0a98f
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id	oai:doaj.org-article:42169163a00e455f87d68247a1a0a98f
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spelling	oai:doaj.org-article:42169163a00e455f87d68247a1a0a98f2021-12-02T19:07:54ZKähler metrics via Lorentzian Geometry in dimension four2300-744310.1515/coma-2020-0002https://doaj.org/article/42169163a00e455f87d68247a1a0a98f2019-11-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0002https://doaj.org/toc/2300-7443Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under certain conditions g and gK share various properties, such as a Killing vector field or a vector field with a geodesic flow. In some cases the Kähler metrics are complete. The Ricci and scalar curvatures of gK are computed under certain assumptions in terms of data associated to g. Many examples are described, including classical spacetimes in warped products, for instance de Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type D such as Kerr and NUT metrics, and metrics for which gK is an SKR metric. For the latter an inverse ansatz is described, constructing g from the SKR metric.Aazami Amir BabakMaschler GideonDe Gruyterarticlekahler metriclorentzian metricsheartwistintegrable complex structureswarped productsde sitter spacetimekerr metricgravitational wavespp wavespetrov type53b3053b5553c55MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 36-61 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	kahler metric lorentzian metric shear twist integrable complex structures warped products de sitter spacetime kerr metric gravitational waves pp waves petrov type 53b30 53b55 53c55 Mathematics QA1-939
spellingShingle	kahler metric lorentzian metric shear twist integrable complex structures warped products de sitter spacetime kerr metric gravitational waves pp waves petrov type 53b30 53b55 53c55 Mathematics QA1-939 Aazami Amir Babak Maschler Gideon Kähler metrics via Lorentzian Geometry in dimension four
description	Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which coincides with M in many typical examples. Under certain conditions g and gK share various properties, such as a Killing vector field or a vector field with a geodesic flow. In some cases the Kähler metrics are complete. The Ricci and scalar curvatures of gK are computed under certain assumptions in terms of data associated to g. Many examples are described, including classical spacetimes in warped products, for instance de Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type D such as Kerr and NUT metrics, and metrics for which gK is an SKR metric. For the latter an inverse ansatz is described, constructing g from the SKR metric.
format	article
author	Aazami Amir Babak Maschler Gideon
author_facet	Aazami Amir Babak Maschler Gideon
author_sort	Aazami Amir Babak
title	Kähler metrics via Lorentzian Geometry in dimension four
title_short	Kähler metrics via Lorentzian Geometry in dimension four
title_full	Kähler metrics via Lorentzian Geometry in dimension four
title_fullStr	Kähler metrics via Lorentzian Geometry in dimension four
title_full_unstemmed	Kähler metrics via Lorentzian Geometry in dimension four
title_sort	kähler metrics via lorentzian geometry in dimension four
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/42169163a00e455f87d68247a1a0a98f
work_keys_str_mv	AT aazamiamirbabak kahlermetricsvialorentziangeometryindimensionfour AT maschlergideon kahlermetricsvialorentziangeometryindimensionfour
_version_	1718377144912969728

Kähler metrics via Lorentzian Geometry in dimension four

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