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Centrifugal acceleration in GR

  1. Dec 23, 2012 #1
    I swing an accelerometer around my head with a constant relative speed of v and a radius of r. I want the exact formula with highly relativistic effects, so v = .8 c and r = 1 meter, say. What proper acceleration will the accelerometer read?
     
  2. jcsd
  3. Dec 23, 2012 #2

    PeterDonis

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    Staff: Mentor

    Take a look at the Wikipedia page on Born coordinates:

    http://en.wikipedia.org/wiki/Born_coordinates

    They give a formula for the proper acceleration of a "Langevin observer", which corresponds to the accelerometer being swung around your head. They give it in terms of the angular velocity [itex]\omega[/itex], but using the formula [itex]v = \omega r[/itex], it is easy to come up with a formula in terms of the velocity [itex]v[/itex]:

    [tex]a = \frac{- v^2}{r \left( 1 - v^2 \right)}[/tex]

    This makes sense; it's just the standard Newtonian formula for centripetal acceleration, with an extra relativistic factor of [itex]\gamma^2[/itex].
     
  4. Dec 23, 2012 #3
    Thank you PeterDonis.
     
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