Einstein Aether Theory - The Action

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

K^{ab}_{mn}=c_1g^{ab}g_{mn}+ c_2\delta^a_m\delta^b_n +c_3\delta^a_n\delta^b_m+c_4u^au^bg_{mn}.

Here the ci are dimensionless adjustable parameters of the theory.

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