General Relativity: An Introduction for Physicists · Problem 12.8
Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby
Physics · uniform-density-star-limits-redshift
Problem
Show that, for a spherical star of uniform density ρ,
R2<3πGρc2andM2<243πρG316c6.
If a photon is emitted from the star's surface and received by a stationary observer at infinity, show that the observed redshift must obey the constraint z<2. Show also, however, that the observed redshift for a photon emitted from the star's centre can be arbitrarily large.