General Relativity: An Introduction for Physicists · Problem 11.13

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · principal-stresses-radial-free-fall

Problem

An unpowered satellite is in radial free fall towards a Schwarzschild black hole. Show that the principal stresses in the satellite are given by

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

In what directions do these principal stresses act? Compare your answer with that obtained in Exercise 11.10.