Relativity energy-momentum tensor

  • Thread starter PineApple2
  • Start date
  • #1
49
0

Homework Statement



Arrive at the orthogonality relation [itex]{T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = K{\delta^{\mu}}_{\nu}[/itex]
and determine K.

Homework Equations


[itex] T_{ij}=T_ji} [/itex]


The Attempt at a Solution


[itex] {T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = {T^{\mu}}_0{T^0}_{\nu}+ {T^{\mu}}_i{T^i}_{\nu}[/itex]
I am not sure how to continue from here, in which direction I should go...
Thanks!
 
Last edited:

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
Insights Author
13,023
576
Is T appearing in the Einstein equations ? If so, use them.
 
  • #3
49
0
No, we haven't even studied yet Einstein's equations (the context is special-relativistic electrodynamics. T is the enrgy-momentum (stress) tensor)
 
  • #4
dextercioby
Science Advisor
Homework Helper
Insights Author
13,023
576
Aaaa, you should have said that. Ok, then you know how T looks like in terms of F. Then just express the contraction in the LHS in terms of F and regroup it so that you'll get a scalar times unit tensor.
 

Related Threads on Relativity energy-momentum tensor

Replies
0
Views
6K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
0
Views
2K
Replies
4
Views
2K
  • Last Post
Replies
13
Views
905
Replies
1
Views
998
Replies
2
Views
1K
Top