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Maxwell's energy-momentum tensor cannot be used as is in Einstein's equation for general relativity in the presence of sources. In this case, its four-divergence is non-zero, whereas the tensors in the equation must have this characteristic. However, the sun emits streams of ionized particles, gases are present within galaxies, material transfers in the form of ionized plasma can occur in binary star systems, and so on. These charges cannot be neglected in the study of space-time in these regions. Here, we present a modified version of this tensor that eliminates this flaw, provided that the potentials satisfy the Lorenz gauge. The distribution of sources will also be analyzed in light of fluid mechanics, allowing us to account for its influence in terms of generated pressure.
Serge Collin (Mon,) studied this question.
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