Optical Geometry of the Kerr Space-time
Mathematical Physics
2011-11-22 v1 General Relativity and Quantum Cosmology
Differential Geometry
Geometric Topology
math.MP
Abstract
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the Gauss Bonnet theorem and its applications to surfaces in optical geometry, as developed by G. W. Gibbons and M. C. Werner. Finally, we attempt to extend this geometrical approach to the axially symmetric Kerr spacetime, and arrive at an expression for the gravitational deflection angle in the equatorial plane.
Keywords
Cite
@article{arxiv.1111.4998,
title = {Optical Geometry of the Kerr Space-time},
author = {Cameron Bloomer},
journal= {arXiv preprint arXiv:1111.4998},
year = {2011}
}