Inspirals from the innermost stable circular orbit of Kerr black holes: Exact solutions and universal radial flow

TL;DR

This paper provides exact solutions for test particle spirals from the ISCO of Kerr black holes, revealing a simple, universal form of radial velocity independent of black hole spin, applicable across all allowed Kerr parameters.

Contribution

It introduces exact, universal solutions for particle orbits from the ISCO in Kerr spacetime, valid for any black hole spin parameter.

Findings

Radial 4-velocity is remarkably simple.

Solutions are universal when scaled by ISCO radius.

Applicable for all allowed Kerr spin values.

Abstract

We present exact solutions of test particle orbits spiralling inward from the innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are valid for any allowed value of the angular momentum $a$-parameter of the Kerr metric. These solutions are of considerable physical interest. In particular, the radial 4-velocity of these orbits is both remarkably simple and, with the radial coordinate scaled by its ISCO value, universal in form, otherwise completely independent of the black hole spin.