New total transmission modes of the Kerr geometry with Schwarzschild limit frequencies at complex infinity

TL;DR

This paper discovers new families of total-transmission modes in Kerr black hole geometries, connecting to complex infinity frequencies at the Schwarzschild limit, and provides numerical and analytical characterizations of these modes.

Contribution

It identifies two new families of total-transmission modes in Kerr geometry, expanding understanding beyond previously known modes and connecting to complex infinity frequencies.

Findings

Numerically constructed mode sequences for harmonic indices 2 to 8.

Derived analytic asymptotic expansions for mode frequencies.

Found that the separation constant's asymptotic expansion applies to complex oblateness values.

Abstract

In addition to the well-known quasinormal modes, the gravitational modes of the Kerr geometry also include sets of total-transmission modes. Each mode can be considered as an element of a sequence of modes parameterized by the angular momentum of the black hole. One family of gravitational total-transmission modes of Kerr have been known for some time. Modes in this family connect to a Schwarzschild limit where the mode frequency is finite and purely imaginary. Recently, what was thought to be an additional branch of this original family of modes was discovered. However, this new branch is actually a part of one of two entirely new families of total-transmission modes. Modes in these new families, surprisingly, connect to a Schwarzschild limit where the mode frequencies exist at complex infinity. We have numerically constructed full sets of sequences of gravitational total-transmission modes for harmonic indices $\ell=[2,8]$. Using these numerical sequences, we have been able to construct analytic asymptotic expansions for the mode frequencies and their associated separation constants. The asymptotic expansion for the separation constant used in constructing the total-transmission modes seems to be valid for general complex values of the oblateness parameter.