Flux-balance laws in scalar self-force theory
arXiv:2209.13829 · doi:10.1103/PhysRevD.108.104029
Abstract
The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of motion. In the presence of spacetime symmetries, the situation simplifies: there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution. Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law. However, there exist constants of motion that are not related to spacetime symmetries, the most notable example of which is the Carter constant in the Kerr spacetime. In this paper, we first present a new approach to flux-balance laws for spacetime symmetries, using the techniques of symplectic currents and symmetry operators, which can also generate more general conserved currents. We then derive flux-balance laws for all constants of motion in the Kerr spacetime, using the fact that the background, geodesic motion is integrable. For simplicity, we restrict derivations in this paper to the scalar self-force problem. While generalizing the discussion in this paper to the gravitational case will be straightforward, there will be additional complications in turning these results into a practical flux-balance law in this case.
arXiv comment15+3 pages, 1 figure; v2: corrected typos and added appendix and figure, "matches" published version
References in corpus (34)
- The motion of point particles in curved spacetime
- Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
- Self-force via a Green's function decomposition
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- Stability of Black Holes and Black Branes
- Hamiltonian of a spinning test-particle in curved spacetime
- Second-order gravitational self-force
- The self-consistent gravitational self-force
- Gravitational self force and gauge transformations
- Prospects for observing extreme-mass-ratio inspirals with LISA
- Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
- Gravitational self-force from radiation-gauge metric perturbations
- Completion of metric reconstruction for a particle orbiting a Kerr black hole
- Hamilton-Jacobi equation for spinning particles near black holes
- Energy conservation for point particles undergoing radiation reaction
- Motion of small objects in curved spacetimes: An introduction to gravitational self-force
- Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
- Dissipation in extreme-mass ratio binaries with a spinning secondary
- Motion in classical field theories and the foundations of the self-force problem
- Hamiltonians and canonical coordinates for spinning particles in curved space-time
- New metric reconstruction scheme for gravitational self-force calculations
- "Flux-balance formulae" for extreme mass-ratio inspirals
- The mass and angular momentum of reconstructed metric perturbations
- The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds
- Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals
- Complete set of quasi-conserved quantities for spinning particles around Kerr
- Angular momentum at null infinity in Einstein-Maxwell theory
- Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?
- Particle motion under the conservative piece of the self-force is Hamiltonian
- Non-conservation of Carter in black hole spacetimes
- A class of conserved currents for linearized gravity in the Kerr spacetime
- Conserved currents for electromagnetic fields in the Kerr spacetime
- Gravitational-wave energy and other fluxes in ghost-free bigravity