Solve TOV for Non-Constant Density Star - Friends Help Needed!

[shadi_s10]

Dear friends,

Does anyone know how we can solve the TOV equations for a non constant density?
In all the references, I just saw the solution for a constant density.
Thanks in advance for the help :)

 

[George Jones]

An equation of state and boundary conditions also are needed. As is often the case with (systems of ) differential equations, few analytical solutions are know. From page 293 of "General Relativity: Am Introduction for Physicists" by Hobson, Efstathiou, and Lasenby:

"Very few exact solutions are known for realistic equations of state, and so in practice the system of equations is integrated numerically on a computer. The procedure is to ‘integrate outwards’ from r = 0 (in practice in small radial steps of size $\delta$r) until the pressure drops to zero. This condition defines the surface r = R of the star, since otherwise there would be an infinite pressure gradient, and hence an infinite force, on the material elements constituting the outer layer of the star"

 

[shadi_s10]

An equation of state and boundary conditions also are needed..."

Thanks for your explanations.
Is using general relativity in order to get to the pressure inside a star OK?
I am doing some calculations and so far I think the gravitational potential would be quit different.