The Action
The action of the Einstein æther theory is generally taken to consist of the sum of the Einstein–Hilbert action with a Lagrange multiplier λ that ensures that the time vector is a unit vector and also with all of the covariant terms involving the time vector u but having at most two derivatives.
In particular it is assumed that the action may be written as the integral of a local Lagrangian density
where GN is Newton's constant and g is a metric with Minkowski signature. The Lagrangian density is
Here R is the Ricci scalar, is the covariant derivative and the tensor K is defined by
Here the ci are dimensionless adjustable parameters of the theory.
Read more about this topic: Einstein Aether Theory
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