Homework Help: Relativity energy-momentum tensor

1. Nov 24, 2011

PineApple2

1. The problem statement, all variables and given/known data

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

2. Relevant equations
$T_{ij}=T_ji}$

3. The attempt at a solution
${T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = {T^{\mu}}_0{T^0}_{\nu}+ {T^{\mu}}_i{T^i}_{\nu}$
I am not sure how to continue from here, in which direction I should go...
Thanks!

Last edited: Nov 24, 2011
2. Nov 24, 2011

dextercioby

Is T appearing in the Einstein equations ? If so, use them.

3. Nov 24, 2011

PineApple2

No, we haven't even studied yet Einstein's equations (the context is special-relativistic electrodynamics. T is the enrgy-momentum (stress) tensor)

4. Nov 25, 2011

dextercioby

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.