A compact 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 = 2.0\,M_\odot

. Take

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

. ((a)) Find its Schwarzschild radius

r_s

. ((b)) Two shells surround it at areal radii

r_1 = 18.0\ \mathrm{km}

and

r_2 = 24.0\ \mathrm{km}

. Find the proper radial distance between them. ((c)) Find the exact redshift

z

for light climbing from a static emitter at

r_1=18.0

km to a distant static receiver, and compare with the first-order estimate.

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