# Definition of stress-energy tensor

• I
Hello! Why is the stress energy tensor defined as a (2 0) tensor? I understand that it needs 2 one-forms as arguments, but using the metric, can't we bring it to (1 1) or (0 2)? So is there is any physical or mathematical reason why it is defined as (2 0), or it is equally right to define it as (1 1) or (2 0)?

pervect
Staff Emeritus
You can use the metric to raise and lower indices on any rank 2 tensor (including the stress-energy tensor), so you can write it as a (2,0), (1,1), or (0,2) tensor. What made you think you couldn't?

dextercioby
Homework Helper
@Silviu: What exact definition of this tensor do you mean? (Dă, te rog, sursa / provide the exact source)

As already stated by the members above, you can raise and lower it the indices on the stress energy tensor as you like. Why the usual stress tensor ##T^{\alpha \beta}## has two upper (or lower indices)? Maybe because the way they are sometimes defined. For a perfect fluid its defined as $$T^{\alpha\beta}=(\rho+P)u^\alpha u^\beta+Pg^{\alpha\beta}.$$
Where:
##u## is the four velocity
##\rho## is themass/energy density
##P## is Pressure
Edit: Definition is for a metric of signature ##(-+++)##

Last edited:
vanhees71