Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors

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Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's ... continued below

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Burns, Michael E. May 2004.

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  • Burns, Michael E.

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Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold.
Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's field equation.

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UNT Student Graduate Works

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  • May 2004

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  • Feb. 15, 2008, 3:11 p.m.

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  • March 24, 2016, 4:48 p.m.

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Burns, Michael E. Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors, thesis, May 2004; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc4532/: accessed April 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .