1305.0475 (Ivan Arraut)

On the astrophysical scales set by the Cosmological Constant    [PDF]

Ivan Arraut

It is already known that a positive Cosmological Constant $\Lambda$ sets the scale $r_0=\left(\frac{3}{2}r_s r_\Lambda^2\right)^{1/3}$, which depending on the mass of the source, can be of astrophysical order of magnitude. This scale was interpreted before as the maximum scale in order to get bound orbits. In this paper I compute the same scale with a different method and obtain its first order correction 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 the corresponding saddle point of the effective potential 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 and $\beta$ is a dimensionless parameter given by $\beta\equiv \frac{L_{max}}{L}$.

View original: http://arxiv.org/abs/1305.0475