When deriving the Einstein field equation from a theory with a dilaton field, we have:
However, in my calculation:
So I found that GHS has missed $R$ and $(▽φ)^2$. When setting $φ->0$, the conventional Einstein-Maxwell equation can be obtained from my equation but not GHS's.
However, all the articles are using GHS's results. It seems I am wrong. Who can explain this?