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General RelativityA Concise Introduction$
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Steven Carlip

Print publication date: 2019

Print ISBN-13: 9780198822158

Published to Oxford Scholarship Online: March 2019

DOI: 10.1093/oso/9780198822158.001.0001

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The weak field approximation

The weak field approximation

(p.66) 8 The weak field approximation
General Relativity

Steven Carlip

Oxford University Press

The Einstein field equations are a complicated set of coupled partial differential equations, which are usually too complicated to find exact solutions. This chapter introduces a simple approximation for weak fields. It discusses the lowest order solution, which gives back Newtonian gravity, and the next order, which includes “gravitomagnetic” or “frame-dragging” effects. The chapter briefly discusses higher order approximations, expansions around a curved background, and the evidence that gravitational energy itself gravitates. It concludes with a brief description of an alternative derivation of the Einstein field equations, starting from flat spacetime and “bootstrapping” the gravitational self-interaction.

Keywords:   frame-dragging, gravitational energy, gravitomagnetism, Lens-Thirring effect, Newtonian limit, Nordtvedt effect, post-Newtonian approximation, spin two, gravity from field theory, weak field approximation

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