TITLE:
Direct and Exact Description of Null Geodesics in Schwarzschild Spacetime
AUTHORS:
Leo Morgovsky
KEYWORDS:
Black Holes, Schwarzschild Metric, Photon Trajectory, Hawking Radiation
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.9 No.1,
January
31,
2023
ABSTRACT: Null geodesics for massless particles in Schwarzschild spacetime are obtained by direct integration of the trajectory equation in spatial coordinates without transformation to the inverse space. The results are classified following Chandrasekhar depending on the ratio of the impact parameter of the trajectory to its critical value. In the subcritical and supercritical cases the geodesics are expressed in terms of elliptic integrals of the first kind. Some results are formally different from the classical ones, but in fact equivalent to them, being at the same time more compact and descriptive.