The Teukolsky--Starobinsky constants: facts and fictions

TL;DR

This paper investigates the properties of Teukolsky--Starobinsky constants in Kerr black hole physics, revealing that they can be negative for spins greater than 2, indicating a new energy amplification phenomenon.

Contribution

It clarifies misconceptions about the constants and demonstrates their potential negativity for higher spins, expanding understanding of field dynamics in black hole spacetimes.

Findings

Constants can be negative for spin > 2

Energy amplification occurs for non-superradiant frequencies

Dispels myths about Teukolsky--Starobinsky constants

Abstract

The Teukolsky Master Equation describes the dynamics of massless fields with spin on a Kerr black hole. Under separation of variables, spin-reversal for this equation is accomplished through the so-called Teukolsky--Starobinsky identities. These identities are associated to the so-called Teukolsky--Starobinsky constants, which are spin-dependent. We collect some properties of the Teukolsky--Starobinsky constants and dispel some myths present in the literature. We show that, contrary to popular belief, these constants can be negative for spin larger than 2. Such fields thus exhibit a novel form of energy amplification which occurs for non-superradiant frequencies.