Non-conservation of Carter in black hole spacetimes

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.

5 pages, 1 figure, (v2) typos corrected, some clarifications and appendix B added

References in corpus (2)

• Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
• Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity

Cited by in corpus (8)

• Hamilton-Jacobi equation for spinning particles near black holes
• "Flux-balance formulae" for extreme mass-ratio inspirals
• Angular momentum at null infinity in Einstein-Maxwell theory
• Flux-balance laws for spinning bodies under the gravitational self-force
• A class of conserved currents for linearized gravity in the Kerr spacetime
• Conserved currents for electromagnetic fields in the Kerr spacetime
• Exploiting the hidden symmetry of spinning black holes: conservation laws and numerical tests
• Flux-balance laws in scalar self-force theory