A compact object 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

A compact object has mass M=3.0 M⊙M = 3.0\,M_\odot. Take GM⊙/c2=1.48 kmGM_\odot/c^2 = 1.48\ \mathrm{km}. ((a)) Find its Schwarzschild radius rsr_s. ((b)) Two shells surround it at areal radii r1=12.0 kmr_1 = 12.0\ \mathrm{km} and r2=18.0 kmr_2 = 18.0\ \mathrm{km}. Find the proper radial distance between them. ((c)) Find the exact redshift for light climbing from a static emitter at r1=12.0r_1=12.0 km to a distant static receiver, and compare with the first-order estimate.

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