A compact stellar remnant has mass

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

M = 1.0\,M_\odot

. Take

GM_\odot/c^2 = 1.48\ \mathrm{km}

. ((a)) Find the Schwarzschild radius

r_s

of the remnant. ((b)) Two spherical shells surround the remnant, with areal radii

r_1 = 10.0\ \mathrm{km}

and

r_2 = 15.0\ \mathrm{km}

. Find the proper radial distance a static observer's ruler measures between the shells. ((c)) Light leaves a static emitter on the shell at

r_1 = 10.0\ \mathrm{km}

and reaches a distant static receiver. Find the exact redshift

z

and compare it with the first-order estimate

GM/r_1c^2

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