General Relativity: An Introduction for Physicists · Problem 11.12

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · tidal-crushing-astronaut

Problem

An astronaut, starting from rest at infinity, falls radially inwards towards a Schwarzschild black hole with

M = 10^5 M_\odot

. Calculate the radial coordinate from the centre of the black hole at which the astronaut first experiences a lateral tidal force of

400\,\text{m}\,\text{s}^{-2}\,\text{m}^{-1}

and is therefore crushed. How does this radial coordinate compare with the position of the event horizon?