Uniform Acceleration and Black Holes

(Lecture: 10 minutes)

• Acceleration in SR is described by hyperbolas
• Can outrun a beam of light!
• This is analogous to a black hole!

See §13.5 of the text.

Reflections

A simple argument shows that constant acceleration corresponds to moving along a hyperbola in spacetime, and that any such hyperbola has an asymptote, corresponding to a beam of light — which therefore never quite catches up. The spacetime diagram which describe this situation are quite similar to those which describe black hole solutions in general relativity — which is not as surprising as it initially appears, since observers at constant radius must be undergoing constant acceleration to prevent themselves from falling.

(This unit needs some further text materials, and especially some figures.)

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