Ricci tensor for electromagnetic field

[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?

 

[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.

 

[ngkamsengpeter]

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?

 

[torquil]

Some info on traceless energy-momentem tensors:

http://www.google.no/url?sa=t&rct=j&q=traceless%20energy&source=web&cd=5&sqi=2&ved=0CFMQFjAE&url=http%3A%2F%2Fitf.fys.kuleuven.be%2Fsupergravity%2Fpdf%2FExtraCh15.pdf&ei=KMWZT62bJYbGtAbW84TSAQ&usg=AFQjCNGfiOyDX9WceFT_TDL8SMoF1bJmng&cad=rja