Renormalized Dynamical Friction in Black-Hole Spacetimes
Abstract
We derive the renormalized local equation of motion for the gravitational self-force on a compact object moving through matter in a black-hole spacetime. We integrate out the environment and metric perturbations on a Schwinger--Keldysh contour, obtaining a causal effective action given by a sum of curved-spacetime Feynman diagrams organized by powers of the mass ratio and environmental density. At leading order, an environmental wake gravitationally backreacts on the worldline. The corresponding diagram contains a logarithmic ultraviolet divergence that renormalizes the leading dissipative fluid--particle coupling. We isolate the divergence with a local large-momentum expansion, in which the curved-spacetime retarded Green's function reduces to its flat tangent-space form. We translate the resulting singularity into a Barack--Ori mode-sum scheme, deriving an analytic puncture and regularization parameters for an ideal-fluid environment. Mode subtraction fixes the divergent part but not the finite Wilson coefficient. For collisionless dust, we determine this coefficient by matching to an exact near-zone calculation for a black hole moving through the medium. This gives a complete renormalization prescription suitable for numerical self-force calculations.
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BibTeX
@misc{wilsongerow2026renormalized,
title = {{Renormalized Dynamical Friction in Black-Hole Spacetimes}},
author = {Jordan Wilson-Gerow},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23192},
eprint = {2609.23192},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23192},
}
RIS
TY - UNPB
TI - Renormalized Dynamical Friction in Black-Hole Spacetimes
AU - Jordan Wilson-Gerow
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23192
UR - https://arxiv.org/abs/2609.23192
AB - We derive the renormalized local equation of motion for the gravitational self-force on a compact object moving through matter in a black-hole spacetime. We integrate out the environment and metric perturbations on a Schwinger--Keldysh contour, obtaining a causal effective action given by a sum of curved-spacetime Feynman diagrams organized by powers of the mass ratio and environmental density. At leading order, an environmental wake gravitationally backreacts on the worldline. The corresponding diagram contains a logarithmic ultraviolet divergence that renormalizes the leading dissipative fluid--particle coupling. We isolate the divergence with a local large-momentum expansion, in which the curved-spacetime retarded Green's function reduces to its flat tangent-space form. We translate the resulting singularity into a Barack--Ori mode-sum scheme, deriving an analytic puncture and regularization parameters for an ideal-fluid environment. Mode subtraction fixes the divergent part but not the finite Wilson coefficient. For collisionless dust, we determine this coefficient by matching to an exact near-zone calculation for a black hole moving through the medium. This gives a complete renormalization prescription suitable for numerical self-force calculations.
ER -