Translation:On the spacetime lines of a Minkowski world

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On the spacetime lines of a Minkowski world (1912)
by Friedrich Kottler, translated from German by Wikisource

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related portals: Relativity

In German: Über die Raumzeitlinien der Minkowski'schen Welt, 1912, Wiener Sitzungsberichte 2a, 121: 1659-1759, Online

Friedrich Kottler2291633On the spacetime lines of a Minkowski world1912Wikisource

On the spacetime lines of a Minkowski world

by

Friedrich Kottler

(Presented at the meeting at 4. July 1912.)

	CONTENTS.
	Page
Introduction. Denotations	1659
§ 1. Integral forms. Differential invariants. Generalized coordinates	1664
§ 2. Applications to $S_{3}$ and $S_{4}$ : Gauss-Stokes theorems. Vector analysis in generalized coordinates	1675
§ 3. Maxwell's equations and the integral forms; Maxwell's equations in generalized coordinates	1685
§ 4. Pointlike charges. Spacetime lines. Formulas of Wiechert and Schwarzschild. Formulas for the displacement of the light-point together with the reference-point. Wiechert-Schwarzschild formulas in generalized coordinates	1691
§ 5. Ponderomotive forces. The reaction force of radiation when the charge is pointlike	1703
§ 6. Special spacetime lines: Curves whose three curvatures are constant. Computation of the potentials and fields in generalized coordinates. Constancy of the fields in the generalized reference system	1714
§ 7. Differential geometry of the curves in $S_{4}$ . Comoving tetrad. Frenet formulas. Two classes of curves	1728
§ 8. Application to the spacetime lines	1749

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