A neutron star has mass and radius

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity

The Geometry of Gravity, Ch The Schwarzschild geometry and Birkhoff's theorem

Problem

A neutron star has mass M=1.6 M⊙M = 1.6\,M_\odot and radius R⋆=10.5 kmR_\star = 10.5\ \mathrm{km}. Take GM⊙/c2=1.48 kmGM_\odot/c^2 = 1.48\ \mathrm{km}. ((a)) Find its Schwarzschild radius rsr_s. ((b)) A shell at r2=15.0 kmr_2 = 15.0\ \mathrm{km} surrounds the star. Find the proper radial distance from the surface (r1=R⋆r_1=R_\star) to this shell. ((c)) Find the exact surface redshift zz (light emitted at r1=R⋆r_1=R_\star, received far away) and compare it with the first-order estimate GM/R⋆c2GM/R_\star c^2.

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