Show that there is exactly one radius at which a light beam can move in a circular

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Show that there is exactly one radius at which a light beam can move in a circular orbit around a spherical black hole, and find this radius. Then show that the orbit is unstable, by showing that a tangential beam beginning at a slightly larger radius will spiral outward and never return, and a tangential beam beginning at a slightly smaller radius will spiral into the black hole.

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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