# Ricci tensor for electromagnetic field

1. Apr 25, 2012

### ngkamsengpeter

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?

Last edited: Apr 25, 2012
2. Apr 25, 2012

### 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.

Last edited: Apr 25, 2012
3. Apr 25, 2012

### ngkamsengpeter

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?

4. Apr 26, 2012