Translation:On the spacetime lines of a Minkowski world

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

related portals: Relativity.

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

2291633On the spacetime lines of a Minkowski world1912Friedrich Kottler

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

This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.

Original:

This work is in the public domain in the United States because it was published before January 1, 1929.

The longest-living author of this work died in 1965, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 58 years or less. This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.

Public domainPublic domainfalsefalse

Translation:

This work is released under the Creative Commons Attribution-ShareAlike 3.0 Unported license, which allows free use, distribution, and creation of derivatives, so long as the license is unchanged and clearly noted, and the original author is attributed.

Public domainPublic domainfalsefalse