General Relativity: An Introduction for Physicists · Problem 12.9

Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby

Physics · star-within-schwarzschild-radius

Problem

For a spherical star of uniform density

\rho

, show that in order for the star not to lie within its own Schwarzschild radius, one requires

M^2 < \frac{3c^6}{32\pi\rho G^3}.

Compare this limit with that derived in Exercise 12.8.