Category Archives: Mathematica

SL(2,R) Killing vector fields in coordinates

Posted on 2017/05/11 by arkajad

In Parametrization of SL(2,R) we introduced global coordinates on the group SL(2,R). Any matrix in SL(2,R) can be uniquely written as (1)   If is the matrix with components then its coordinates can be expressed as functions of the matrix … Continue reading →

Posted in Hyperbolic geometry, Mathematica, SU(1,1) | 3 Comments

Curvature of the upper half-plane

Posted on 2017/05/05 by arkajad

In Geodesics on upper half-plane factory direct we used the Christoffel symbols and identified geodesics on the upper half plane endowed with the hyperbolic geometry metric. The formulas for Christoffel symbols contain derivatives of the metric tensor components: (1)   … Continue reading →

Posted in Hyperbolic geometry, Mathematica | 2 Comments

Einstein the Stubborn

Posted on 2017/05/03 by arkajad

Before developing his 1915 General Theory of Relativity, Einstein held the “Entwurf” theory. Tullio Levi-Civita from Padua, one of the founders of tensor calculus, objected to a major problematic element in this theory, which reflected its global problem: its field … Continue reading →

Posted in Hyperbolic geometry, Mathematica | 1 Comment