Abstract
Abstract Chapter 10 pursues the Newtonian correspondence further and reformulates Newtonian theory in such a way that it leads naturally to the particular set of field equations of general relativity. A number of thought experiments, including the famous lift experiments, which were important to Einstein in deriving the field equations are considered. The non-local lift thought experiments are introduced and it is shown how they indicates that a non-uniform gravitational field may be detected through the relative acceleration of nearby particles. The mathematical formulation of this is through the equation of geodesic deviation and it is shown how, by analogy with the Newtonian equation, this leads to the vacuum field equations of general relativity. The final section shows how these need to be modified to be consistent with both the conservation of energy–momentum and the contracted Bianchi identities.
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