1201.5611 (Uros Kostic)

Analytical time-like geodesics    [PDF]

Uros Kostic

Time-like orbits in Schwarzschild space-time are presented and classified in
a very transparent and straightforward way into four types. The analytical
solutions to orbit, time, and proper time equations are given for all orbit
types in the form r=r(\lambda), t=t(\chi), and \tau=\tau(\chi), where \lambda\
is the true anomaly and \chi\ is a parameter along the orbit. A very simple
relation between \lambda\ and \chi\ is also shown. These solutions are very
useful for modeling temporal evolution of transient phenomena near black holes
since they are expressed with Jacobi elliptic functions and elliptic integrals,
which can be calculated very efficiently and accurately.

View original: http://arxiv.org/abs/1201.5611