On the astrophysical scales set by the Cosmological Constant

It is already known that a positive Cosmological Constant $\Lambda$ sets the scale $r 0=\left\frac{3}{2}r s r \Lambda^2 ight^{1-3}$, which depending on the mass of the source, can be of astrophysical order of magnitude. This scale was interpreted before as the maximum distance in order to get bound orbits. In this paper I compute $r 0$ with a different method and obtain its first order correction $r 0$ due to the angular momentum $L$ of the test particle moving around the source. I then re derive by using more rigorous methods the maximum angular momentum in order to get bound orbits $L {max}=\frac{1}{4}9r s^2r {\varLambda}^{1-3}$ and its corresponding saddle point position given by $r x=\frac{1}{2}3r s r \Lambda^2^{1-3}$, here $r s=2GM$ is the Schwarzschild radius, $r \Lambda=\frac{1}{\sqrt{\Lambda}}$ is the Cosmological Constant scale.

Author: Ivan Arraut

Source: https://archive.org/