Relativistic dynamical friction in Kerr-Schild coordinates
Abstract
Simulations of the evolution of matter on static metric backgrounds allow us to estimate backreaction effects like dynamical friction at first order in the matter density. Previous simulations of dynamical friction have used boosted isotropic and quasi-isotropic Kerr coordinates, which simplifies the extraction of the relevant diagnostics but results in a more complicated implementation of the evolution. In particular, the lack of horizon penetrating coordinates means that high resolutions are needed to ensure convergence, and the boosted, spinning black hole metric cannot easily be written in a closed form, making it more costly to evaluate. In this paper we describe how to reformulate the calculation of the diagnostics in the boosted Kerr-Schild frame for the non-spinning case. We verify that our implementation reproduces previous results quantifying dynamical friction in wave-like dark matter in the appropriate regimes. We discuss the subtleties of transforming diagnostic observables between frames in a 3+1 evolution and develop a general framework for this process.
Related
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BibTeX
@misc{wang2026relativistic,
title = {{Relativistic dynamical friction in Kerr-Schild coordinates}},
author = {Zipeng Wang and Francesca Chadha-Day and Katy Clough and James Maxwell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13684},
eprint = {2610.13684},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13684},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relativistic dynamical friction in Kerr-Schild coordinates
AU - Zipeng Wang
AU - Francesca Chadha-Day
AU - Katy Clough
AU - James Maxwell
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13684
UR - https://arxiv.org/abs/2610.13684
AB - Simulations of the evolution of matter on static metric backgrounds allow us to estimate backreaction effects like dynamical friction at first order in the matter density. Previous simulations of dynamical friction have used boosted isotropic and quasi-isotropic Kerr coordinates, which simplifies the extraction of the relevant diagnostics but results in a more complicated implementation of the evolution. In particular, the lack of horizon penetrating coordinates means that high resolutions are needed to ensure convergence, and the boosted, spinning black hole metric cannot easily be written in a closed form, making it more costly to evaluate. In this paper we describe how to reformulate the calculation of the diagnostics in the boosted Kerr-Schild frame for the non-spinning case. We verify that our implementation reproduces previous results quantifying dynamical friction in wave-like dark matter in the appropriate regimes. We discuss the subtleties of transforming diagnostic observables between frames in a 3+1 evolution and develop a general framework for this process.
ER -