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Home » eq 0 \), we solve: - Simpleprint

eq 0 \), we solve: - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 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:

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

📌 Under a Lorentz boost along the x-axis with velocity \(v\), the metric tensor remains \( \eta^{\mu

📌 u} = ext{diag}(1, -1, -1, -1) \), and the transformation matrix \(\Lambda\) is:

📌 \[ \Lambda = egin{pmatrix} \gamma & -\gamma v & 0 & 0 \ -\gamma v & \gamma & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{pmatrix} \]

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