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Global variational methods in general relativity with applications to gravitational lensing
Author(s) -
Giani Fabio
Publication year - 1999
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199912)8:10<849::aid-andp849>3.0.co;2-d
Subject(s) - morse theory , physics , morse code , gravitation , general relativity , theoretical physics , manifold (fluid mechanics) , gravitational lens , variational principle , theory of relativity , classical mechanics , computer science , mathematics , pure mathematics , quantum mechanics , galaxy , mechanical engineering , telecommunications , redshift , engineering
In this note we give an idea of two of the more important theories concerning global variational methods, namely Ljusternik‐Schnirelmann Theory and Morse Theory. Thanks to them it is possible, in many different situations, to link the topological properties of a given manifold X with the number of critical points of the funcionals defined on X . We show, as example, how to apply Morse Theory to obtain a mathematical description of the gravitational lens effect.