Scalar wave scattering by black holes embedded in dark matter halos
Abstract
We study the scattering of massless scalar waves by static black holes embedded in dark matter halos. The halo is modelled by means of a Hernquist profile, for which the Einstein equations admit an exact solution. We analyse the scattering using null geodesics, the glory approximation, the partial wave expansion, and the complex angular momentum (CAM) method. The geometric analysis shows that the presence of the halo changes the light ring radius weakly but shifts the critical and glory impact parameters. The wave analysis shows that the characteristic black hole interference pattern is preserved, with halo compactness providing the leading correction and the halo scale radius playing a secondary role. For sufficiently compact halos, the environment also induces a sizeable gravitational redshift. Most of the displacement of the interference extrema can be reproduced by a vacuum Schwarzschild solution with an appropriately chosen ωMBH. A non-vanishing residual, however, reveals a genuine halo contribution that cannot be absorbed into such an effective frequency shift. Finally, we perform the CAM reconstruction of the scattering cross section and find that only a few Regge poles are required to achieve high accuracy at large angles.
Related
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BibTeX
@misc{hu2026scalar,
title = {{Scalar wave scattering by black holes embedded in dark matter halos}},
author = {Shi-Qian Hu and Federico Piazza},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01391},
eprint = {2609.01391},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05742646v1},
}
RIS
TY - UNPB
TI - Scalar wave scattering by black holes embedded in dark matter halos
AU - Shi-Qian Hu
AU - Federico Piazza
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.01391
UR - https://hal.science/hal-05742646v1
AB - We study the scattering of massless scalar waves by static black holes embedded in dark matter halos. The halo is modelled by means of a Hernquist profile, for which the Einstein equations admit an exact solution. We analyse the scattering using null geodesics, the glory approximation, the partial wave expansion, and the complex angular momentum (CAM) method. The geometric analysis shows that the presence of the halo changes the light ring radius weakly but shifts the critical and glory impact parameters. The wave analysis shows that the characteristic black hole interference pattern is preserved, with halo compactness providing the leading correction and the halo scale radius playing a secondary role. For sufficiently compact halos, the environment also induces a sizeable gravitational redshift. Most of the displacement of the interference extrema can be reproduced by a vacuum Schwarzschild solution with an appropriately chosen ωM_BH. A non-vanishing residual, however, reveals a genuine halo contribution that cannot be absorbed into such an effective frequency shift. Finally, we perform the CAM reconstruction of the scattering cross section and find that only a few Regge poles are required to achieve high accuracy at large angles.
ER -