On the Earth the tides result from the changing of the gravitational forces exerted by the Sun and Moon from one side of the Earth to the other. By extension, we refer to any effect of the variation of a gravitational force as a tidal effect. Near a black hole, the gravitational force should fall off very quickly with small changes in distance from the surface. We write the acceleration of gravity as a function of radius g(r) = GM/r2

Differentiating with respect to r gives dg(r)/dr = — 2GM/r3 (8.13)

Though the gravitational force falls off as 1/r2, the tidal effects fall off as 1/r3, meaning that they are most important for small values of r.

Example 8.3 Black hole tidal forces Find the difference between the acceleration of gravity at the feet and head of an astronaut just outside a 1M0 black hole.

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