Figure 1

Schwarzschild and Schwarzschild-de Sitter geometries. ${\Sigma }^3$ is the Flamm paraboloid representation of a central coordinate plane in Schwarzschild spacetime; ${\Sigma }^2$ is the corresponding surface in Schwarzschild-de Sitter spacetime; ${\Sigma }^1$ is an auxiliary plane with an $r$, $\varphi$ graph, ${\mathcal{L}}^1$, of the orbit equation (9). The curves ${\mathcal{L}}^2$ and ${\mathcal{L}}^3$ are the vertical projections of ${\mathcal{L}}^1$ onto ${\Sigma }^2$ and ${\Sigma }^3$, and represent the true spatial curvature of the orbits.Reuse & Permissions

Figure 2

The orbital map. This is a plane graph of the orbit equation (9) and coincides with ${\Sigma }^1$ in Fig. 1. The one-sided deflection angle is $\psi -\varphi \equiv ϵ$.Reuse & Permissions