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39 - The Einstein Action and the Einstein Equation

from Part III - Other Spins or Statistics; General Relativity

Published online by Cambridge University Press:  04 March 2019

Horaƫiu Năstase
Affiliation:
Universidade Estadual Paulista, São Paulo
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Summary

We start by defining the notion of Riemann tensor and curvature, and positive and negative curvature spaces. We then show how to turn a special relativistic invariant theory into a general relativistic invariant one and write down the Einstein–Hilbert action for gravity, based on Einstein's principles and on matching with experiment. We then derive its equations of motion, Einstein's equations. We give examples of usual energy–momentum tensors in curved space and end by interpreting the Einstein's equations.

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Publisher: Cambridge University Press
Print publication year: 2019

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