Non-conservation of Carter in black hole spacetimes

TL;DR

This paper disproves the conjecture that Carter's constant conservation extends to general processes with conserved stress-energy tensors in Kerr black hole spacetimes, showing no such universal conservation law exists.

Contribution

It provides a rigorous proof that Carter's constant conservation does not generalize to arbitrary energy-momentum conserving processes in Kerr backgrounds.

Findings

Carter conservation law applies only to point particles, not general stress-energy tensors.

No universal conservation law reduces to Carter's constant for all processes.

The conjecture that Carter's constant conservation extends broadly is false.

Abstract

Freely falling point particles in the vicinity of Kerr black holes are subject to a conservation law, that of their Carter constant. We consider the conjecture that this conservation law is a special case of a more general conservation law, valid for arbitrary processes obeying local energy momentum conservation. Under some fairly general assumptions we prove that the conjecture is false: there is no conservation law for conserved stress-energy tensors on the Kerr background that reduces to conservation of Carter for a single point particle.