## Ricci tensor for electromagnetic field

Electromagnetic fields mostly have a stress-energy tensor in which the trace is zero. Is traceless stress energy tensor always implies Ricci scalar is zero? If yes how to prove that?

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 Recognitions: Gold Member Yes. Just contract the EFE's: $g^{\mu \nu }R_{\mu \nu}-\frac{1}{2}g^{\mu \nu }g_{\mu \nu }R=\kappa g^{\mu \nu } T_{\mu \nu }$ $R^\mu_{~\mu}-\frac{1}{2}\delta^{\mu}_{~\mu} R=\kappa T^{\mu}_{~\mu}$ $R=- \kappa T^{\mu}_{~\mu}$ EDIT: I probably should have said yes, assuming no cosmological constant.

 Quote by elfmotat Yes. Just contract the EFE's: $g^{\mu \nu }R_{\mu \nu}-\frac{1}{2}g^{\mu \nu }g_{\mu \nu }R=\kappa g^{\mu \nu } T_{\mu \nu }$ $R^\mu_{~\mu}-\frac{1}{2}\delta^{\mu}_{~\mu} R=\kappa T^{\mu}_{~\mu}$ $R=- \kappa T^{\mu}_{~\mu}$ EDIT: I probably should have said yes, assuming no cosmological constant.
Ok. Thanks. What is the physical meaning of traceless Ricci scalar or stress energy tensor? Why would the electromagnetic field have a traceless stress energy tensor?

## Ricci tensor for electromagnetic field

Some info on traceless energy-momentem tensors: