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The reason why I think trace of energy-momentum tensor can't be the source is that, in a static weak field $p$<<$\rho$

$$T^{\mu}_{\mu} \approx T^{0}_{0} = -\rho$$

and if in one system I have only $T^0_0$ component, this won't be true for all systems. Therefore, trace of energy-momentum tensor is not a good candidate.

According to what it was written in the following paper, it has something to do with coupling of gravity to electromagnetic field but I don't see how

http://www.cpt.univ-mrs.fr/~cosmo/SW_2013/PPT/Novello.pdf

"The source of scalar gravity is the trace of the energy-momentum tensor: this originates the main handicap of all previous scalar gravity: gravity does not couple to the electromagnetic field."

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Such a theory disagrees with experiment. There would be no gravitational waves and coupling to a free electromagnetic wave would be impossible, as the trace of its EM tensor is zero.

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  • $\begingroup$ Thank you for your answer, can you elaborate what you meant by "coupling to free electromagnetic wave would be impossible" ? Trace of EM tensor is zero but how is it related to energy-momentum tensor in GR? $\endgroup$ – Monopole Jan 6 at 13:02

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