# Tagged Questions

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### Tensors in special relativity [duplicate]

I'm trying to understand tensors, but I've come across the following question: Let $T^{\mu\nu}$ by a $(2,0)$ tensor. Give the definitions of $T_\mu^{\,\nu}$, $T_{\mu\nu}$, and ...
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### Pressure and Density Using a General Lagrangian

Given a lagrangian of a form: $$\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)$$ where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
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### Chern-Simons Energy-Momentum Tensor

I'm assuming the following statement is true. I'm not finding any reference which shows that explicitly. Statement: Chern-Simons term is a topological one and does not contribute to the ...
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Let $T_{ab}$ be a stress-tensor in a flat space satisfying conservation equations. Define $$P^i=\int T^{oi}d^3x, \;\; D^i=\int T^{00}x^id^3x$$ Can anyone show me how to prove $$\frac{dD^i}{dt}=P^i ... 2answers 275 views ### Einstein equation and scalar field stress-energy tensor Let's have interaction between gravitational and scalar real fields. For an action of gravitational field in vacuum I add term S_{m} = \int d^{4}x\sqrt{-g}L_{m}, where$$ L_{m} = \frac{1}{2}g^{\mu ...
I read somewhere that stress-energy tensor density is a symmetric tensor. But if I take the Dirac Field tensor: $$T^{\mu \nu}=i \psi^\dagger \gamma^0 \gamma^\mu \partial^\nu \psi$$ How could I ...
Having a bit of trouble applying what I know about tensor manipulation, given, $T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$, I need to compute quantities ...