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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 ##(-+++)##

Where:

##u## is the four velocity

##\rho## is themass/energy density

##P## is Pressure

Edit: Definition is for a metric of signature ##(-+++)##

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