General Relativity: An Introduction for Physicists · Problem 12.10

Further spherically symmetric geometries — Hobson, Efstathiou & Lasenby

Physics · spatial-sections-uniform-density-star

Problem

For a spherical uniform-density star of mass

M

and coordinate radius

R

, show that the line element of spatial sections with

t =

constant can be written in the form

d\sigma^2 = \frac{Rc^2}{2GM}\left[d\chi^2 + \sin^2\chi\left(d\theta^2 + \sin^2\theta\, d\phi^2\right)\right].