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Neutron Star Cooling

The Star's structure in GR: Hydrostatic Equilibrium

GR Version Equations

• Mass $$\frac{dm}{dr} = 4\pi r^2 \rho$$

• Gravitational Potential $$\frac{d\Phi}{dr} = \frac{Gmc^2 + 4\pi G r^3 P}{c^4r^2(1 - 2Gm/c^2r)}$$

• Hydrostatic Equlibrium (Tolman-Oppenheimer-Volkoff eqution) $$\frac{dP}{dr} = -(\rho c^2 + P)\frac{d\Phi}{dr}-\frac{(\rho + P/c^2)(Gm + 4\pi Gr^3P/c^2)}{(r^2(1-2Gm/c^2r))}$$

$$(\Phi = \Phi_r = \frac{1}{c^2}\phi)~~\text{is the gravitational potential}$$