MTW section 25, from eq. 25.16 onwards, derives an orbital equation (with G=c=1, u = M/r, E and L Schwarzschild constants for energy and angular momentum respectively):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left(\frac{du}{d\phi}\right)^2 = \frac{M^2}{L^2}(E^2-1) + \frac{2M^2}{L^2}u - u^2 + 2u^3 [/tex]

This equation is readily differentiable to give

[tex]\frac{d^2u}{d\phi^2}= \frac{M^2}{L^2} - u + 3u^2 [/tex]

which is often used for numerical integration to obtain orbital plots of [itex]r[/itex] against [itex]\phi[/itex].

My question: since both equations seem to be well behaved for any [itex]u < \infty[/itex], can they be used to plot the 'infalling' orbit inside the horizon? Or are either E or L or both not valid there?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orbit eq. holds inside BH?

Loading...

Similar Threads - Orbit holds inside | Date |
---|---|

I How can General Relativity explain the Moon drifting apart from Earth | Mar 3, 2018 |

I Using Black Holes to Time Travel Into the Future | Feb 4, 2018 |

A Black hole orbit inequality | Jan 6, 2018 |

I Can two gravitational waves orbit each other? | Oct 7, 2017 |

The sun attractive to the earth and holds us in orbit. | Oct 5, 2003 |

**Physics Forums - The Fusion of Science and Community**