# TOV equations inside a star with non constant density

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1. Aug 11, 2015

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 :)

2. Aug 11, 2015

### George Jones

Staff Emeritus
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"

3. Sep 15, 2015