Determination of the metric of a Schwarzschild black hole surrounded by a halo of dark matter

[2606.27482] Determination of the metric of a Schwarzschild black hole surrounded by a halo of dark matter Skip to main content Search Submit Donate Log in General Relativity and Quantum Cosmology arXiv:2606.27482 (gr-qc) [Submitted on 25 Jun 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Determination of the metric of a Schwarzschild black hole surrounded by a halo of dark matter Authors: M. Castillo Alarcón , Leonel Bixano , I. A. Sarmiento-Alvarado , Claudio Salas-Pérez , Tonatiuh Matos View PDF HTML (experimental) Abstract: Following the landmark acquisition of the first image of a black hole, systems comprising a black hole enveloped by a dark matter halo have attracted considerable attention. This work implements a novel method to analyze the structure of a system composed of a Schwarzschild black hole and a dark matter halo modeled as an anisotropic fluid, while ensuring that the proposed metric constitutes an exact solution of the Einstein field equations. Numerical results show that the connection between the temporal and radial metric functions preserves an inverse relationship, namely $A(r) \approx 1/B(r)$. Furthermore, we analytically demonstrate that the resulting functions satisfy $A(r)B(r) = 1 + \mathcal{O}(10^{-6})$, in excellent agreement with the numerical findings. In addition, the Einstein equations imply that the variation of the product $A(r)B(r)$ is governed by the factor $\varepsilon_h=\frac{8\pi G\rho_0r_0^2}{c^2}$. Finally, we show that the interior Schwarzschild region and the exterior dark matter halo can be joined smoothly via a regular Darmois Israel junction, without generating any thin shell curvature steps. To assess the observational implications of the model, we compare its theoretical predictions for the pericenter precession of the S2 star and the angular size of the shadow of Sgr A*. In both cases, the predicted deviations remain within the observational uncertainties reported by the GRAVITY Collaboration and the Event Horizon Telescope (EHT), respectively. These results demonstrate that the proposed black hole dark matter halo configuration is not only mathematically consistent, but also compatible with current observational constraints. Comments: 6 figures, 15 pages Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Astrophysics of Galaxies (astro-ph.GA) MSC classes: 83F05, 85A05, 83C57 Cite as: arXiv:2606.27482 [gr-qc] (or arXiv:2606.27482v2 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2606.27482 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mayte Castillo Alarcón [ view email ] [v1] Thu, 25 Jun 2026 19:05:38 UTC (1,721 KB) [v2] Thu, 27 Aug 2026 18:20:59 UTC (1,725 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-06 Change to browse by: astro-ph astro-ph.GA References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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