Jump to ContentJump to Main Navigation
Relativity, Gravitation and CosmologyA Basic Introduction$
Users without a subscription are not able to see the full content.

Ta-Pei Cheng

Print publication date: 2009

Print ISBN-13: 9780199573639

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199573639.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 23 May 2019

GR as a geometric theory of gravity — II

GR as a geometric theory of gravity — II

(p.318) 14 GR as a geometric theory of gravity — II
Relativity, Gravitation and Cosmology

Ta-Pei Cheng

Oxford University Press

The mathematical realization of equivalence principle (EP) is the principle of general covariance. General relativity (GR) equations must be covariant with respect to general coordinate transformations. To go from special relativity (SR) to GR equations, one replaces ordinary by covariant derivatives. The SR equation of motion turns into the geodesic equation. The Einstein equation, as the relativistic gravitation field equation, relates the energy momentum tensor to the Einstein curvature tensor. The Einstein equation in the space exterior to a spherical source is solved to obtain the Schwarzschild solution. The solutions of Einstein equation that satisfy the cosmological principle is the Robertson-Walker spacetime. The relation of the cosmological Friedmann equations to the Einstein field equation is explicated. The compatibility of the cosmological-constant term with the mathematical structure of Einstein equation and the interpretation of this term as the vacuum energy tensor are discussed.

Keywords:   principle of general covariance, general relativity, geodesic equation, Einstein equation, Newtonian limit, Schwarzschild solution, Robertson-Walker spacetime, cosmological constant

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .