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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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

📌 The stress-energy tensor in the original frame is given by:

📌 u} = egin{pmatrix} \sigma & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \end{pmatrix} \]

📌 The trace of the tensor is:

📌 \[ T^{\mu}_{\mu} = T^{0}_{0} + T^{1}_{1} + T^{2}_{2} + T^{3}_{3} = \sigma + 0 + 0 + 0 = \sigma \]

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