Classify the conservative and dissipative components of the matter-response self-force

Classify the matter-response self-force into its dissipative dynamical-friction component and any conservative remainder by completing a flux-balance analysis of the energy and angular-momentum transfer to the environment.

Background

The paper distinguishes the complete matter-response sector of the environmental gravitational self-force from the subset identified as dynamical friction. The former requires a dynamical response from the environment but is not necessarily dissipative, so the authors do not yet have a definitive classification of all of its contributions.

A flux-balance formulation, analogous to the asymptotic gravitational-wave flux balance used in vacuum self-force theory, is proposed as the means to determine which matter-response terms represent dissipation and which constitute a conservative remainder. This analysis would also provide an independent route to computing dynamical friction.

References

It requires the environment's dynamical response but need not be dissipative, whose classification is left open pending the flux-balance analysis discussed above.

— Dynamical Friction as Environmental Gravitational Self-Force  (2608.24800 - Datta, 25 Aug 2026) in Conclusions, following Eq. (hierarchy)

A secondary black hole however will accrete matter from the environment, making its mass dynamical. As a result the force may receive an additional contribution that has not been explored here. Whether this accretion induced contribution is already captured by the criterion above, or requires extending the underlying force law to a dynamical-mass secondary remains to be studied.

— Dynamical Friction as Environmental Gravitational Self-Force  (2608.24800 - Datta, 25 Aug 2026) in Conclusions, paragraph beginning “Unlike prior relativistic treatments”