Construct rotating line-distribution and thin-disk perturbations of Kerr

Investigate the construction of stationary, axially symmetric perturbations of a Kerr black hole generated by arbitrary line distributions of rotating matter along the symmetry axis, including rotating rings or thin disks, within linear perturbation theory.

Background

The paper derives closed-form Weyl–Lewis–Papapetrou metric functions from Debye potentials for stationary and axially symmetric perturbations of Kerr. For a rotating point particle on the symmetry axis, the reconstructed metric contains a string that can be removed on only one side of the particle. Because the perturbation equations are linear, the authors observe that the point-particle construction can be extended to arbitrary line distributions of matter along the symmetry axis. Such distributions could then be used to generate rotating disks around the Kerr black hole, generalizing earlier exact but static disk constructions; the proposed extension would remain valid only to linear perturbation order.

References

Owing to the linearity of the problem, we can construct the perturbation of the Kerr black hole not only by a single point particle, but by an arbitrary line distribution of matter along the symmetry axis. Such a field can then be used to generate a disk around the black hole, much as in Refs.; there, however, the results are exact but static, whereas the construction outlined here would yield a rotating disk, albeit only to the linear perturbation order. We leave a more detailed investigation to future work.

— Reconstruction of the Weyl-Lewis-Papapetrou metric for stationary and axially symmetric gravitational perturbations of a Kerr black hole  (2608.24096 - Kofroň et al., 25 Aug 2026) in Section 4.2, “Rotating point particle on the axis”