The TOV equation for hydrostatic equilibrium in general relativity can be written as…

PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Relativistic stars and compact objects · Relativistic stars and compact objects

Stars from the Inside, Ch Neutron stars and pulsars: the densest matter, the maximum mass and the spinning magnet

Problem

The TOV equation for hydrostatic equilibrium in general relativity can be written as the Newtonian equation multiplied by three correction factors: dPdr=−Gmρr2(1+Pρc2)(1+4πr3Pmc2)(1−2Gmrc2)−1.\frac{\mathrm{d}P}{\mathrm{d}r} = -\frac{Gm\rho}{r^2}\left(1+\frac{P}{\rho c^2}\right)\left(1+\frac{4\pi r^3P}{mc^2}\right)\left(1-\frac{2Gm}{rc^2}\right)^{-1}. Near the centre of a neutron star, m=43πr3ρm = \tfrac{4}{3}\pi r^3\rho, so the second factor becomes 1+3P/ρc21 + 3P/\rho c^2, and the third factor tends to 11 as r→0r \to 0. At a point inside a neutron star where P/ρc2=0.15P/\rho c^2 = 0.15, evaluate the product of the three TOV correction factors and state how much harder gravity pulls there than the Newtonian formula alone would predict.

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