= Scalar equation of Brans-Dicke theory
{title2=$(2\omega+3)\Box\Phi=8\pi G T$}
Assume four spacetime dimensions, $\Phi\ne0$, constant $\omega$, no <scalar> potential and matter independent of $\Phi$. In the stated action convention, <scalar> <variation> gives $\Phi R+\omega\Phi^{-1}(\nabla\Phi)^2-2\omega\Box\Phi=0$. The <trace> of the <metric tensor> equation gives $\Phi R+\omega\Phi^{-1}(\nabla\Phi)^2+3\Box\Phi=8\pi G T$. Their subtraction proves the displayed <wave equation> with $T=g^{ab}T_{ab}$. The <degenerate coupling of Brans-Dicke theory> needs separate treatment before dividing by its coefficient.
Back to article page
