Astrophysical properties of Bertrand spacetime

In classical mechanics Bertrand\'s theorem specifies the kind of potentials which can give rise to closed, stable circular orbits. One can generalize the results of Bertrand\'s theorem in special relativity where the particle moving in the potential can have high speeds. There has been a generalization of Bertrand\'s theorem in general relativity where one can have certain spacetimes called Bertrand spacetimes (BSTs). From each point on the spatial hypersurface of a BST there can pass a closed, stable circular orbit. These spacetimes can have very interesting properties as far as galactic astrophysics is concerned. The talk will focus on the astrophysical properties of BSTs and will particularly focus on the issues concerning velocity rotation curves in low surface brightness galaxies and lensing of light from galaxies and galaxy clusters.