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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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The Einstein equations

The Einstein equations

(p.431) 4 The Einstein equations
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if the gravitational field created by the matter can be neglected, the appropriate framework for describing the matter is that of special relativity. Einstein gravitational equations relate geometry and matter: specifically, they relate the Riemann tensor, or more precisely the Einstein tensor, to the geometrical object describing ‘inertia’, the energy content of the matter—that is, the energy–momentum tensor. These equations form a set of ten nonlinear partial differential equations. The coordinate system can be chosen arbitrarily.

Keywords:   Einstein equations, Minkowski spacetime, gravitational field, special relativity, Einstein gravitational equations, geometry, matter, Riemann tensor, Einstein tensor, energy–momentum tensor

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