Geodesics in Schwarzschild Space
Geodesics in Schwarzschild Space
The right-hand side of the graphic in this Demonstration shows a geodesic outside the Schwarzschild radius , while the left-hand side shows the effective radial potential. The latter depends on the value of the angular momentum , which you can vary with the first slider. The effective radial potential also depends on : a particle orbit has , a null geodesic (such as a light-ray) has , and a time-like geodesic has . You can specify the starting point of the integration for both energy and radius by clicking on an allowed value, on or above the curve on the left.
r
s
ℓ
K
K=1
K=0
K=-1
The two remaining controls, "maximum " and "zoom", specify the length of proper integration time and the zoom scale for the graphic on the right.
τ