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As you may know from some other thread, I was interested through the week in finding a general way of express the energy-momentum tensor that appears in one side of the Einstein's equation.

After much trials, I found that

$$T^{\sigma \nu} = g^{\sigma \nu} \frac{\partial \mathcal{L}}{\partial \partial_{\mu} \phi} \partial_{\nu} \phi - g^{\sigma \nu} \delta^{\mu}{}_{\nu} \mathcal{L}$$ where ##\mathcal{L}## is the Lagrangian density.

As I haven't found an expression like this one on web, I'm unsure about its validity in Relativity.

I would appreciate if someone could tell me whether this expression is valid or not.

I can post here links to the pdf's I have read and how I arrived at the above result.

After much trials, I found that

$$T^{\sigma \nu} = g^{\sigma \nu} \frac{\partial \mathcal{L}}{\partial \partial_{\mu} \phi} \partial_{\nu} \phi - g^{\sigma \nu} \delta^{\mu}{}_{\nu} \mathcal{L}$$ where ##\mathcal{L}## is the Lagrangian density.

As I haven't found an expression like this one on web, I'm unsure about its validity in Relativity.

I would appreciate if someone could tell me whether this expression is valid or not.

I can post here links to the pdf's I have read and how I arrived at the above result.

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