Conformal Geodesics
نویسندگان
چکیده
منابع مشابه
A Conformal Extension Theorem based on Null Conformal Geodesics
In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient order along a congruence of null conformal geodesic. This article extends earlier work by Tod and ...
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We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.
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In the complex-Riemannian framework we show that a conformal manifold containing a compact, simply-connected, null-geodesic is conformally flat. In dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold as the conformal infinity of a selfdual four-manifolds. We also find a relation between the conformal invariants of the conformal infinity and its ambient.
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The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off–diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of the Einstein equations describing ”black ellipsoid” objects [1]. This is possi...
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We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature (1, 1). We will investigate the properties of the solutions of these equations and try to relate the conformal invariant dimension of the space of harmonic and twistor spinors to the natural conformal invariants given by the Lorentzian metric. We wil...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1939
ISSN: 0002-9947
DOI: 10.2307/1990011