- #1

Bishal Banjara

- 90

- 3

- TL;DR Summary
- Generally, the Stress energy tensor is obtained from the Lagrangian. But is it possible to obtain matter Lagrangian (Lm) from the Stress energy tensor?

Basically, the stress energy tensor is given by $$T_{uv}=-2\frac{\partial (L\sqrt{-g})}{\partial g^{uv}}\frac{1}{\sqrt{-g}}.$$ It makes easy to calculate stress energy tensor if the variation of Lagrangian with the metric tensor is known. But it is possible to retrieve matter Lagrangian if the stress energy tensor is known? Is one of the possible way to solve is taking the integration of the above equation?

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