Could you help understand this solution? It seems like they did not solve the problem self consistently, but tried some kind of a matching at a boundary. But if the black hole accretes matter according to Bondi, it will lead to an inhomogeneous matter density and the solution will not be consistent with the homogeneous assumption outside.

why not make a more realistic estimate by setting $M_{\rm big}=10^{10}M_{\rm Sun}$ which exists and calculate the inspiral time from a radius of say $6.6M_{\rm big}$ to $6.0M_{\rm big}$. Is this still very large?

@safesphere how do you resolve the "paradox" that changing the spin parameter $a$ from 0 by an extremely small amount changes the number of light signals received from an external lighthouse by the infalling transiting observer from a finite number to infinity?

@Wookie The book by O'Neill, "The geometry of black holes" reviews literature nicely showing that for the Kerr spacetime only the equatorial timelike geodesics with Carter constant Q=0 hit the singularity, all others avoid the singularity and have a finite curvature everywhere along the curve. The question specifically asked to consider the "maximally extended Kerr spacetime" and geodesics reaching the $r_-$ horizon. Am I missing your point? google.co.uk/books/edition/The_Geometry_of_Kerr_Black_Holes/…

In the Kerr black hole the singularity is a ring and you can go around or through it without getting destroyed.

The papers linked here claim to have proven that the Kerr solution is not unstable quantamagazine.org/…

Can you link papers that prove the instability of the infinite tower of the Kerr solution or is this an assumption based on the results for the charged black holes

It may not be unstable see recent paper cited here wired.com/story/…

Is this an assumption or are there analytical calculations or numetical simulations showing this?

I don't understand this result, The total flux of the cross term cannot go to zero as this would violate energy conservation given that there is work done on the dipole.

Thanks. I'd like to see explicitly the total outgoing energy in radiation as a function of direction at distance $r\rightarrow\infty$ and see that when integrating over the sphere this is increased by $-q\vec{E}_{\rm ext}\cdot\vec{v}$, relative to the case when $\vec{E}_{\rm ext}=0$.

Thanks @knzhou, what I am confused by is that the rotating dipole radiation field has an infinitesimal total power across an infinitesimally narrow angle around the axis, so I don't see how the interference term of this with the plane wave may be finite. Also, the analogous stimulated absorbtion implies that you can cast a narrow shadow with an object much smaller than a wavelength?

Nice answer, but the part on the direction of stimulated emission was unclear. Is there a reason for this for non-quantum systems? Could you please take a look at this related question? physics.stackexchange.com/questions/736445/…

It seems to me that this answer is wrong, given that stimulated emission can be produced during resonant scattering by a classical dipole, see physics.stackexchange.com/questions/736445/…