Black Hole Orbit Inequality: Explained

[quasarLie]

Hello,
Here's an interesting question inspired by a homework probem (not mine), we know that circular orbit (for scjwarzchild black hole) exist only if L ≥ sqrt3 c Rsch=Lisco . Where does this inequality come from? do you have a lecture which can help me to understand?
Thanks

 

[mfb]

Circular orbit or stable circular orbit?

To find the closest stable orbit you can look at the effective potential. In Newtonian mechanics this always has a minimum, in GR you get a 1/r³ term (if I remember correctly) that ruins the minimum below this critical L. For lower L you have a potential that goes down all the way to the black hole.

 

[m4r35n357]

Hello,
Here's an interesting question inspired by a homework probem (not mine), we know that circular orbit (for scjwarzchild black hole) exist only if L ≥ sqrt3 c Rsch=Lisco . Where does this inequality come from? do you have a lecture which can help me to understand?
Thanks

It is covered by equations 7.29 to 7.55 in Carrol's online notes.