Mentor
2019 Award
In this article we will analyze “centrifugal force reversal” in Kerr spacetime, similar to what was done for Schwarzschild spacetime in a previous Insights article. As our starting point, we will use the formulas for the frame field, proper acceleration, and vorticity of an observer in a circular orbit in the equatorial plane of Kerr spacetime that we derived in our study of Fermi-Walker transport. These formulas are:
$$\hat{p}_0 = \frac{1}{D} \partial_t + \frac{\omega}{D} \partial_\phi = \gamma \hat{h}_0 + \gamma v \hat{h}_3$$
$$\hat{p}_1 = \partial_z$$
$$\hat{p}_2 = W \partial_r$$
$$\hat{p}_3 = \frac{\omega r H^2 – B}{W D} \partial_t + \frac{V^2 + \omega r B}{r W D} \partial_\phi = \gamma v \hat{h}_0 + \gamma \hat{h}_3$$
$$A = \frac{W}{D^2} \left[ \frac{M}{r^2} \left( 1 – a \omega \right)^2 – \omega^2 r \right]$$
$$\Omega = \frac{1}{D^2} \omega \left[ 1 – \frac{3M}{r} \left( 1 – a \omega \right) \right] + \frac{M a}{r^3 D^2} \left( 1 – a \omega \right)^2$$
where we...