High spin expansion for null geodesics

TL;DR

This paper develops an analytical high spin expansion method for null geodesics in Kerr spacetime, providing insights into black hole observations like M87* and highlighting the method's limitations near extremality.

Contribution

It introduces a high spin expansion approach for null geodesics in Kerr spacetime, with analytical radial integrals, sensitive to the Carter constant, applicable to astrophysical black holes.

Findings

Analytical expressions for radial integrals are derived.

Method is effective for large Carter constant q.

Applicability is limited near extreme black holes.

Abstract

We consider the high spin expansion for the null geodesics in the Kerr spacetime. We expand the null geodesic equation successively to higher orders in deviation from extremity. Via the method of matched asymptotic expansion, the radial integrals are obtained analytically. It turns out that the analytic expressions are very sensitive to the value of the shifted Carter constant $q$. We show that for a large $q$, the analytic expressions can be used to study observational electromagnetic signatures for astrophysical black holes like M87*. However, for a small $q$, the high spin expansion method can only be applied to (near-) extreme black holes.