Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Accelerations in Kerr Metric

  1. Dec 5, 2009 #1


    User Avatar
    Science Advisor
    Gold Member

    Pervect has https://www.physicsforums.com/showpost.php?p=1046874&postcount=17" for radial and tangential gravitational accelerations of a moving particle in Schwarzschild coordinates.

    \frac{d^2 r}{d t^2} = \frac {3 m{{\it v_r}}^{2}}{ \left( r-2\,m \right) r} + \left( r-2\,m \right) \left( {{\it v_\phi}}^{2}-{\frac {m}{{r}^{3}}} \right)

    \frac{d^2\phi}{d t^2} = -\frac {2 {\it v_r}\,{\it v_\phi}\, \left( r -3\,m \right) }{ \left( r-2\,m \right) r}

    where [itex]v_r =dr/dt[/itex], [itex]v_\phi = d\phi/dt[/itex], [itex]m[/itex] the mass of the primary and [itex]r,\phi[/itex] the Schwarzschild coordinate parameters.

    Does anyone know of an equivalent set of equations for the Kerr metric, at least for movement along the equator of a rotating black hole?
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Jul 21, 2011 #2
    I know that this is a seriously old thread but it remains unanswered. The following paper looks at gravitational acceleration for moving objects in Kerr metric-


    'Geometric transport along circular orbits in stationary axisymmetric spacetimes'

    Donato Bini, Christian Cherubini, Gianluca Cruciani, Robert T. Jantzen

    (Submitted on 1 Jul 2004)

    'Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.'
  4. Jul 21, 2011 #3


    User Avatar
    Science Advisor
    Gold Member

    Thanks Steve, it looks promising!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Accelerations Kerr Metric Date
I Do rotating singularities experience radial acceleration? Sunday at 5:46 PM
I Any theoretical limit on acceleration? Mar 15, 2018
B Gravity and Acceleration Mar 7, 2018
B Kerr black holes Jan 10, 2018
I The rising railway coach Oct 26, 2017