Principal Killing strings in higher-dimensional Kerr-NUT-(A)dS spacetimes

We construct special solutions of the Nambu-Goto equations for stationary strings in a general Kerr-NUT-(A)dS spacetime in any number of dimensions. This construction is based on the existence of explicit and hidden symmetries generated by the principal tensor which exists for these metrics. The characteristic property of these string configurations, which we call “principal Killing strings,” is that they are stretched out from “infinity” to the horizon of the Kerr-NUT-(A)dS black hole and remain regular at the latter. We also demonstrate that principal Killing strings extract angular momentum from higher-dimensional rotating black holes and interpret this as the action of an asymptotic torque.

Figure 1

Torque alignment procedure for the four-dimensional case: The angular momentum 2-form $\mathit{J}=Ma\mathrm{d}x\wedge \mathrm{d}y$ corresponds to the 3-vector ${\partial }_z$ pointing along the $z$-axis. For a string with parameters of point 1 on $S_{\infty }^2$, first create a second string at point 2 to compensate the out-of-plane component of the torque. Then, add the two strings at points 3 and 4 to cancel the net force while keeping the net torque aligned to $\mathit{J}$.