ERIC Number: EJ896425
Record Type: Journal
Publication Date: 2010-Jul
Abstractor: As Provided
Forces in General Relativity
Ridgely, Charles T.
European Journal of Physics, v31 n4 p949-960 Jul 2010
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced by an observer in general coordinates. The general force is then applied to the local co-moving coordinate system of a uniformly accelerating observer, leading to an expression of the inertial force experienced by the observer. Next, applying the general force in Schwarzschild coordinates is shown to lead to familiar expressions of the gravitational force. As a more complex demonstration, the general force is applied to an observer in Boyer-Lindquist coordinates near a rotating, Kerr black hole. It is then shown that when the angular momentum of the black hole goes to zero, the force on the observer reduces to the force on an observer held stationary in Schwarzschild coordinates. As a final consideration, the force on an observer moving in rotating coordinates is derived. Expressing the force in terms of Christoffel symbols in rotating coordinates leads to familiar expressions of the centrifugal and Coriolis forces on the observer. It is envisioned that the techniques presented herein will be most useful to graduate level students, as well as those undergraduate students having experience with general relativity and tensor analysis.
Descriptors: Undergraduate Students, Space Sciences, Textbooks, Astronomy, Science Instruction, Physics, College Science, Scientific Principles, Motion, Graduate Students, Equations (Mathematics)
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: Students; Teachers
Authoring Institution: N/A