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As the first physical example of application using the principle of equivalence and tensor calculus, we want to derive the equation of motion for a particle in a gravitational field. In the local inertial system, the laws of Special Relativity apply, i.e., for a force-free timelike particle with mass m > 0 and worldline \(\vec{x}\left( {t_{E} } \right)\) , the relativistic Newtonian equation of motion 14.12 on page 305 follows:

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Motion in the Gravitational Field, Geodesic Equation

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  • 发表日期：

    2026年

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  • Michael Ruhrländer

摘要

As the first physical example of application using the principle of equivalence and tensor calculus, we want to derive the equation of motion for a particle in a gravitational field. In the local inertial system, the laws of Special Relativity apply, i.e., for a force-free timelike particle with mass m > 0 and worldline \(\vec{x}\left( {t_{E} } \right)\) , the relativistic Newtonian equation of motion 14.12 on page 305 follows: