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Effective potential for timelike Schwarzschild geodesics

For equatorial timelike motion with specific angular momentum

h

,

\frac{1}{2} \overset{r}{˙}^{2} + V_{eff} (r) = \frac{E ^{2} - 1}{2}, V_{eff} = - \frac{m}{r} + \frac{h ^{2}}{2 r ^{2}} - \frac{m h ^{2}}{r ^{3}} .

A circular orbit has

h^{2} = m r^{2} / (r - 3 m)

and therefore requires

r > 3 m

.

Table of contents 50 1
- Schwarzschild perihelion precession Effective potential for timelike Schwarzschild geodesics 23

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