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einstein's equations

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39 - The Einstein Action and the Einstein Equation
from Part III - Other Spins or Statistics; General Relativity
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 367-377
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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.