Editing Neutron star (section)

=== Tolman-Oppenheimer-Volkoff Equation ===
The [[Tolman–Oppenheimer–Volkoff equation|Tolman-Oppenheimer-Volkoff (TOV) equation]] can be used to describe a neutron star. The equation is a solution to Einstein's equations from general relativity for a spherically symmetric, time invariant metric. With a given equation of state, solving the equation leads to observables such as the mass and radius. There are many codes that numerically solve the TOV equation for a given equation of state to find the mass-radius relation and other observables for that equation of state.

The following differential equations can be solved numerically to find the neutron star observables:<ref>{{cite journal |last1=Silbar |first1=Richard R. |last2=Reddy |first2=Sanjay |title=Neutron stars for undergraduates |journal=American Journal of Physics |date=1 July 2004 |volume=72 |issue=7 |pages=892–905 |doi=10.1119/1.1703544|arxiv=nucl-th/0309041 |bibcode=2004AmJPh..72..892S }}</ref>

<math display="block">\frac{dp}{dr} = - \frac{G\epsilon(r) M(r)}{c^2 r^2} \left(1+\frac{p(r)}{\epsilon(r)}\right) \left(1+\frac{4\pi r^3p(r)}{M(r)c^2}\right) \left(1-\frac{2GM(r)}{c^2r}\right)</math>
<math display="block">\frac{dM}{dr} = \frac{4\pi}{c^2} r^2 \epsilon(r)</math>

where <math>G</math> is the gravitational constant, <math>p(r)</math> is the pressure, <math>\epsilon(r)</math> is the energy density (found from the equation of state), and <math>c</math> is the speed of light.