Singular transformations of coordinates In the Schwarzschild metric and interpretation of radial coordinates

Author: papuna nemsitsveridze
Keywords: singular Lagrangian, Schwarzschild metric
Annotation:

The bachelor thesis is devoted to the comparison of Hamilton-Jacob and Euler-Lagrange methods in Schwarzschild space. The generalized Dirac method for constrained systems with singular Lagrangians, for which Legendre transformations are incorrect, is discussed. In the Schwarzschild metric, the Lagrangian of the geodesics is written and its singular nature is shown. It is suggested that the mentioned problem is caused by an incorrect interpretation of the Schwarzschild radial coordinate. The Lagrangian of the geodesics is rewritten in Lemaitre and Kruskal coordinates, which are non-singular on the event horizon. It is shown that the Lagrangian singularity does not disappear in these coordinates, thus we confirm that the Euler-Lagrange and Hamilton-Jacob methods are not equivalent in the Schwarzschild metric.