Summary
We have considered Einstein equations in harmonic coordinates and we have shown that the equations governing relativistic strings are the necessary and sufficient conditions required to preserve harmonicity condition during motion. Moreover, it has been shown that the equations governing strings written in a time-like transverse gauge are the same as the equations governing Born-Infeld electrodynamics with radiation gauge.
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Strumia, A. Einstein equations, relativistic strings and Born-Infeld electrodynamics. Il Nuovo Cimento B 110, 1497–1504 (1995). https://doi.org/10.1007/BF02849848
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DOI: https://doi.org/10.1007/BF02849848