When deriving the Einstein field equation from a theory with a dilaton field, we have:

GHS's calculation GHS's calculation

However, in my calculation:

My calculation 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?

  • 2
    $\begingroup$ Welcome to PSE. Please write formulas using MathJax instead of posting an image of hand-writing. $\endgroup$ – Thomas Fritsch Mar 24 at 17:11
  • $\begingroup$ The lhs of GHS equation is Ricci tensor, not Einstein. Therefore the rhs is not $T_{\mu\nu}$ but $T_{\mu\nu}-\frac 12 T g_{\mu\nu}$. $\endgroup$ – A.V.S. Mar 24 at 18:59

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