Neutron Star Cooling

January 5, 2019 · View on GitHub

The Star's structure in GR: Hydrostatic Equilibrium

GR Version Equations

  • Mass dmdr=4πr2ρ\frac{dm}{dr} = 4\pi r^2 \rho

  • Gravitational Potential dΦdr=Gmc2+4πGr3Pc4r2(1−2Gm/c2r)\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) dPdr=−(ρc2+P)dΦdr−(ρ+P/c2)(Gm+4πGr3P/c2)(r2(1−2Gm/c2r))\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))}

(Φ=Φr=1c2ϕ)  is the gravitational potential(\Phi = \Phi_r = \frac{1}{c^2}\phi)~~\text{is the gravitational potential}