When relativistic mass meets hyperbolic geometry. (English) Zbl 1235.83010

Ungar, Abraham A.

Commun. Math. Anal. 10, No. 1, 30-56 (2011).

Summary: It is admitted in the literature on special relativity that, being velocity dependent, relativistic mass is a wild notion in the sense that it does not conform with the Minkowskian four-vector formalism. The resulting lack of clear consensus on the basic role of relativistic mass in special relativity has some influence in diminishing its use in modern books. Fortunately, relativistic mechanics is regulated by the hyperbolic geometry of Bolyai and Lobachevsky just as classical mechanics is regulated by Euclidean geometry. Guided by analogies that Euclidean geometry and classical mechanics share with hyperbolic geometry and relativistic mechanics, the objective of this article is to tame the relativistic mass by placing it under the umbrella of the Minkowskian formalism, and to present interesting consequences.

MSC:

83A05	Special relativity
51M10	Hyperbolic and elliptic geometries (general) and generalizations

Keywords:

hyperbolic geometry; special relativity; relativistic mass; particle system; center of momentum