Chapter

Riemannian Geometry

Valeri P. Frolov and Andrei Zelnikov

in Introduction to Black Hole Physics

Published in print September 2011 | ISBN: 9780199692293
Published online January 2012 | e-ISBN: 9780191731860 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199692293.003.0003
Riemannian Geometry

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The key notions of the differential and Riemannian geometry necessary for understanding the General Relativity are introduced here. We provide the reader with the necessary tools for study the properties of black holesand their interaction with matter and fields. We tried to omit unnecessary details and to make the presentation simpler. We focus on an explanation of the basic concepts and explicit formulas, which can be used for concrete calculations, and give hints, which might be used to simplify these calculations.

Keywords: differential manifold; Riemannian geometry; curvature tensor; covariant derivative; symmetry; Killing‐Yano tensor

Chapter.  21606 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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