# That tensor from GR - what do we call it?

You know the one I mean, Tμν.1 Is it the stress-energy tensor, or the energy-momentum tensor? This is for the purposes of tags, where having both is redundant. This was brought up in chat, and there is a proposal on our little-visited tag synonyms page. However, it was pointed out there that the idea of just combining everything into won't work due to character limits.

Moreover, I dare anyone to claim with a straight face that they would actually say "stress-energy-momentum tensor" in conversation.

I therefore propose that one of or be taken to be "standard," with the other made a synonym. My understanding is that either tag can then be applied, with the synonym silently being replaced, no harm done, no retagging effort necessary.

Rather than proposing a synonym on my own, only to have no one look at that page anyway,2 I figure this proposal should get some community consensus as to which way the replacement should go. I personally grew up learning that "stress-energy" was a tensor and "energy-momentum" was a 4-vector, but perhaps I'm in the minority, or perhaps there's good reason to differentiate as much as possible the stress-energy tensor of relativity from the stress tensor of mechanics.

1 Yes, I am fully aware that string of symbols refers to an unspecified component of a tensor, and not an actual tensor. Mathematically precise people, please don't hurt me. Everyone else, I still reserve the right to admonish you for conflating these two things :P

2 There are plenty of other suggestions there - interested users should vote on them!

• I suggest we call it Geoffrey. – Wouter Jun 26 '13 at 23:10
• No but I've only seen the energy-momentum 4-vector, I'll be attending a GR course next semester. So I'm not in a position to judge, really. However, I would go for stress-energy-tensor on the basis of causing less confusion alone. Energy-momentum is a SR 4-vector, stress-energy a GR tensor. That makes for a nice, clear distinction. – Wouter Jun 26 '13 at 23:13
• "Moreover, I dare anyone to claim with a straight face that they would actually say "stress-energy-momentum tensor" in conversation." I do. – Abhimanyu Pallavi Sudhir Jun 27 '13 at 13:55
• How about mass-energy-momentum-pressure-stress tensor? – Ben Crowell Jun 27 '13 at 20:08
• @BenCrowell: The Stress-Energy-Momentum Tensor involves mass (multiplied by $c_0^2$), momentum, shear stress, and, pressure. So, I would classify pressure and shear stress as "stress" so stress-mass-momentum tensor. 28 characeters... What about sigma-m-p tensor? 16 characters only! – Abhimanyu Pallavi Sudhir Jun 28 '13 at 8:51
• What about tensor-describing-energy-often-called-the-stress-energy-tensor-or-the-energy-momentum-tensor-or-the-stress-energy-momentum-tensor-or-in-short-comma-the-s-e-m-tensor-or-the-1-by-kappa-einstein-tensor-open-bracket-by-the-einstein-field-equations-or-in-short-comma-the-e-f-e-G-underscore-open-brace-backslash-mu-backslash-nu-close-brace-divided-by-kappa-is-equal-to-T-underscore-open-brace-backslash-mu-backslash-nu-close-brace-close-bracket-and-is-also-called-G-underscore-open-brace-backslash-mu-backslash-nu-close-brace-divided-by-kappa-or-the-einstein-tensor-divided-by-kappa ? – Abhimanyu Pallavi Sudhir Jun 28 '13 at 10:18
• That was 590 characters (I minus-ed the things other than the-tags.) – Abhimanyu Pallavi Sudhir Jun 28 '13 at 10:19
• Personally, I haven't read enough physics texts to have an overview of what is more common. But I would like to point out that Wikipedia already redirects Energy momentum tensor to Stress-energy tensor, for what it's worth. They may not be a particularly true source of knowledge, but the fact is that people who are not well familiar with a term frequently search it there, so they may have an influence of what gets to be the more popular term for the broad mass of search engine users. – rumtscho Jun 29 '13 at 21:24
• Have a nice red [status-completed] tag :) – Manishearth Jul 1 '13 at 3:23
• Strictly speaking, I would call it energy-momentum-density-flow-tensor. – Emilio Pisanty Jul 2 '13 at 19:26

Let's go with as the preferred version and administer the synonymization .

• I agree with this. I have heard/read of SE much more than EM. I dunno why, because to me momentum is usually a much more fundamental thing than stress :P (Yes, I know the context of stress in GR and it's not exactly stress) – Manishearth Jun 26 '13 at 20:58
• I think "stress-energy tensor" is by far the more common usage. Penrose is an example of someone who prefers "energy-momentum tensor." – Ben Crowell Jun 27 '13 at 20:06
• June 30th, 2013: SET proposal leads EMT proposal by votes 15-2. Synonym EMT->SET created. – Qmechanic Jun 30 '13 at 19:27

Let's go with as the preferred version and administer the synonymization .