Carter's constant revealed
Kjell Rosquist, Tomas Bylund, Lars Samuelsson
TL;DR
This paper presents a new formulation of Carter's constant for geodesic motion in Kerr black holes, linking it to total angular momentum and quadratic momentum components, with potential applications in gravitational wave studies.
Contribution
It introduces an exact new form of Carter's constant that simplifies understanding of particle dynamics around Kerr black holes.
Findings
Carter's constant is expressed as total angular momentum plus a quadratic momentum term.
The formulation is exact in the weak gravitational field limit.
Potential usefulness in modeling EMRI systems emitting gravitational waves.
Abstract
A new formulation of Carter's constant for geodesic motion in Kerr black holes is given. It is shown that Carter's constant corresponds to the total angular momentum plus a precisely defined part which is quadratic in the linear momenta. The characterization is exact in the weak field limit obtained by letting the gravitational constant go to zero. It is suggested that the new form can be useful in current studies of the dynamics of extreme mass ratio inspiral (EMRI) systems emitting gravitational radiation.
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