# Is minimal coupling needed for covariant energy conservation?

1. Apr 3, 2013

### atyy

Thanks. I started a new thread, because I've seen what seemed to me a contradictory claim in Carroll's GR notes (Eq 5.38) - he says diff invariance is enough to get covariant energy conservation. I've never understood whether Carroll's claims and the ones in these papers are really contradictory, and if so which are correct. Let me think about what you wrote, and ask more questions later.

2. Apr 3, 2013

### Ben Niehoff

Well, for one, Carroll wasn't talking about $f(R)$ gravity, which is an alternative research topic you linked to in those papers. But the first of your papers shows that even in $f(R)$ gravity, one gets conservation of the EM tensor, provided you define it as "everything else" as I have above.

3. Apr 3, 2013

### atyy

Well, Carroll makes the point that one doesn't need the EP to get covariant energy conservation. Since when talking about the EP, one is usually talking about a class of theories which includes f(R) gravity, I think the main difference is the definitions of the EM tensor. I looked at papers citing the ones in the OP, and there doesn't seem to be any controversy about the result.

What are the motivations for the various definitions of the EM tensor? Perhaps one reason for the alternative EM tensor definition is that the motion of test particles can be derived from it, something like in http://arxiv.org/abs/0704.1733 or http://arxiv.org/abs/0811.0913 ?

Last edited: Apr 3, 2013