Phase transition for a black hole with matter fields and the relation with the Lyapunov exponent

[2604.00753] Phase transition for a black hole with matter fields and the relation with the Lyapunov exponent Skip to main content Search Submit Donate Log in General Relativity and Quantum Cosmology arXiv:2604.00753 (gr-qc) [Submitted on 1 Apr 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Phase transition for a black hole with matter fields and the relation with the Lyapunov exponent Authors: Pakhlavon Yovkochev , Bobomurat J. Ahmedov , Bum-Hoon Lee , Hocheol Lee , Wonwoo Lee View PDF HTML (experimental) Abstract: We construct static black hole solutions coexisting with anisotropic matter in asymptotically (anti-)de Sitter spacetime and investigate how the matter field modifies their thermodynamic and dynamical properties. The anisotropic matter generates an exponentially decaying charge-like contribution to the metric, causing the geometry to interpolate between the Schwarzschild black hole in anti-de Sitter spacetime and the Reissner-Nordström black hole in anti-de Sitter spacetime. In anti-de Sitter black hole spacetime, we derive the complete thermodynamic description, including the Hawking temperature, heat capacity, Smarr relation, generalized first law, and Helmholtz free energy. The system exhibits a van der Waals-type small/large black hole phase transition with a critical point determined by the matter field parameters. Local thermodynamic stability is characterized by the heat capacity, whereas global stability is determined through the free energy. We further investigate unstable homoclinic orbits by evaluating the Lyapunov exponent associated with null geodesics. Our analysis reveals that different thermodynamic branches possess distinct dynamical instabilities, and that the thermodynamically preferred phase is accompanied by a smaller Lyapunov exponent. These results demonstrate that thermodynamic stability and geodesic instability are correlated because both originate from the same underlying spacetime geometry. Comments: 28 pages, 10 figures, ref. papers added, typos are corrected Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th) Report number: CQUeST-2026-0781 Cite as: arXiv:2604.00753 [gr-qc] (or arXiv:2604.00753v2 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2604.00753 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Eur. Phys. J. Plus 141, 979 (2026) Related DOI : https://doi.org/10.1140/epjp/s13360-026-08210-6 Focus to learn more DOI(s) linking to related resources Submission history From: Wonwoo Lee [ view email ] [v1] Wed, 1 Apr 2026 11:18:37 UTC (1,474 KB) [v2] Fri, 28 Aug 2026 06:52:41 UTC (1,601 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-04 Change to browse by: hep-th 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. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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