# Einstein's Field equations and impulse-energy tensor

I premise that I haven't yet studied General Relativity, but in Relativistic Electrodymaics I have knowed impulse-energy tensor of Electromagnetic Field.

I know in Einstein's equations there is impulse-energy tensor $T_{\mu\nu}$ too:

$$R_{\mu \nu} - {1 \over 2} g_{\mu \nu} R + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}$$

I suppose that it's connected with matter in the space, being that equation about gravitation theory.

My question is: has got any sense put in the Einstein's field equation the impulse-energy tensor of EM field? If yes, what is the physical meaning? What are the consequences?

-

## 1 Answer

The stress-energy tensor $T_{\mu\nu}$ on the right side of the Einstein equation characterizes all of the various forms of "stuff" in the spacetime. If there are electromagnetic fields in the spacetime, then the stress-energy tensor of the electromagnetic field is part of that $T_{\mu\nu}$, along with contributions from other forms of energy, mass, etc.

-
Hmm...so EM fields generate gravitational fields? If yes, how can they do this, photons haven't mass...And the gravitational field can have any influence on EM field too? – Boy Simone Feb 5 '11 at 20:32
Yes, EM fields gravitate. Mass is not necessary for something to gravitate -- all forms of energy and momentum gravitate. That's the meaning of the fact that the stress-energy tensor sits on the right of the Einstein equation. Finally, yes, the gravitational field influences the EM field, in much the same way that it influences other forms of matter. For instance, starlight (waves of EM field) is bent by the mass of the Sun. This is Eddington's great experimental result that confirmed general relativity and made Einstein famous. – Ted Bunn Feb 5 '11 at 20:35
OK thank you for your relevant and interesting answer! – Boy Simone Feb 5 '11 at 20:55