Energy-momentum Tensor: Noether vs Hilbert

Akio Hosoya; Shunsuke Fujii

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arXiv · 2403.17457

Energy-momentum Tensor: Noether vs Hilbert

Akio Hosoya·Shunsuke Fujii

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Abstract

We revisit the old problem of the energy-momentum tensor in general relativistic field theories. On the basis of the general covariance we derive a simple equation for the Hilbert and Noether energy-momentum tensors for the scalar and electromagnetic field theories. We see that the two definitions of energy-momentum tensors coincide and identify the Noether current if the space-time has the Killing vector. Relation to the Wald entropy is also briefly discussed.

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Akio Hosoya, Shunsuke Fujii. 2024-03-26. Energy-momentum Tensor: Noether vs Hilbert. https://arxiv.org/abs/2403.17457

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