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#### 25**Question:
A materials scientist is analyzing the behavior of a self-healing polymer under stress. The stress-energy tensor for the material is given by \( T^{\mu
u} = ext{diag}(\sigma, 0, 0, 0) \), where \(\sigma\) is the isotropic stress component. If the material is transformed by a Lorentz boost along the x-axis with velocity \(v\), find the trace of the transformed tensor \( T'^{\mu
u} \).
The stress-energy tensor in the original frame is given by:
\[ T^{\mu
u} = egin{pmatrix} \sigma & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \end{pmatrix} \]