General Relativity: An Introduction for Physicists · Problem 11.14

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · principal-stresses-circular-orbit

Problem

An unpowered satellite follows a circular orbit of radius

r

around a Schwarzschild black hole. Show that the principal stresses in the satellite are given by

\frac{\mu c^2}{r^3}\frac{2r-3\mu}{r-3\mu}, \qquad -\frac{\mu c^2}{r^3}\frac{r}{r-3\mu}, \qquad -\frac{\mu c^2}{r^3}.

In what directions do these principal stresses act?