Energy-momentum Tensor: Noether vs Hilbert

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.

After further confirmation of other published papers, we found that our paper is not new. Thus we are going to withdraw our paper from arXiv