{"title":"ModMax AdS黑洞的Lyapunov指数、相变和混沌界","authors":"Gorima Bezboruah, Mozib Bin Awal, Prabwal Phukon","doi":"10.1140/epjc/s10052-025-14920-5","DOIUrl":null,"url":null,"abstract":"<div><p>We study the thermodynamic phase transition of ModMax anti-de Sitter (AdS) black holes using Lyapunov exponents of massless and massive particles in unstable circular orbits. Our results demonstrate that the thermal profile of the Lyapunov exponent serves as an efficient probe of the black hole’s phase structure. We calculate the discontinuity in the Lyapunov exponent across the transition and show that it acts as an order parameter, exhibiting a critical exponent <span>\\(\\delta =1/2\\)</span> in the vicinity of the critical point. Furthermore, we explore the violation of the chaos bound, finding that the bound is violated when the horizon radius falls below a threshold value. We also examine how the ModMax parameter and the particle’s angular momentum modify this threshold, revealing their role in controlling the onset of chaos bound violation.\n</p></div>","PeriodicalId":788,"journal":{"name":"The European Physical Journal C","volume":"85 10","pages":""},"PeriodicalIF":4.8000,"publicationDate":"2025-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-025-14920-5.pdf","citationCount":"0","resultStr":"{\"title\":\"Lyapunov exponents, phase transitions, and Chaos bound of ModMax AdS black holes\",\"authors\":\"Gorima Bezboruah, Mozib Bin Awal, Prabwal Phukon\",\"doi\":\"10.1140/epjc/s10052-025-14920-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the thermodynamic phase transition of ModMax anti-de Sitter (AdS) black holes using Lyapunov exponents of massless and massive particles in unstable circular orbits. Our results demonstrate that the thermal profile of the Lyapunov exponent serves as an efficient probe of the black hole’s phase structure. We calculate the discontinuity in the Lyapunov exponent across the transition and show that it acts as an order parameter, exhibiting a critical exponent <span>\\\\(\\\\delta =1/2\\\\)</span> in the vicinity of the critical point. Furthermore, we explore the violation of the chaos bound, finding that the bound is violated when the horizon radius falls below a threshold value. We also examine how the ModMax parameter and the particle’s angular momentum modify this threshold, revealing their role in controlling the onset of chaos bound violation.\\n</p></div>\",\"PeriodicalId\":788,\"journal\":{\"name\":\"The European Physical Journal C\",\"volume\":\"85 10\",\"pages\":\"\"},\"PeriodicalIF\":4.8000,\"publicationDate\":\"2025-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1140/epjc/s10052-025-14920-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal C\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjc/s10052-025-14920-5\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, PARTICLES & FIELDS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal C","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjc/s10052-025-14920-5","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
Lyapunov exponents, phase transitions, and Chaos bound of ModMax AdS black holes
We study the thermodynamic phase transition of ModMax anti-de Sitter (AdS) black holes using Lyapunov exponents of massless and massive particles in unstable circular orbits. Our results demonstrate that the thermal profile of the Lyapunov exponent serves as an efficient probe of the black hole’s phase structure. We calculate the discontinuity in the Lyapunov exponent across the transition and show that it acts as an order parameter, exhibiting a critical exponent \(\delta =1/2\) in the vicinity of the critical point. Furthermore, we explore the violation of the chaos bound, finding that the bound is violated when the horizon radius falls below a threshold value. We also examine how the ModMax parameter and the particle’s angular momentum modify this threshold, revealing their role in controlling the onset of chaos bound violation.
期刊介绍:
Experimental Physics I: Accelerator Based High-Energy Physics
Hadron and lepton collider physics
Lepton-nucleon scattering
High-energy nuclear reactions
Standard model precision tests
Search for new physics beyond the standard model
Heavy flavour physics
Neutrino properties
Particle detector developments
Computational methods and analysis tools
Experimental Physics II: Astroparticle Physics
Dark matter searches
High-energy cosmic rays
Double beta decay
Long baseline neutrino experiments
Neutrino astronomy
Axions and other weakly interacting light particles
Gravitational waves and observational cosmology
Particle detector developments
Computational methods and analysis tools
Theoretical Physics I: Phenomenology of the Standard Model and Beyond
Electroweak interactions
Quantum chromo dynamics
Heavy quark physics and quark flavour mixing
Neutrino physics
Phenomenology of astro- and cosmoparticle physics
Meson spectroscopy and non-perturbative QCD
Low-energy effective field theories
Lattice field theory
High temperature QCD and heavy ion physics
Phenomenology of supersymmetric extensions of the SM
Phenomenology of non-supersymmetric extensions of the SM
Model building and alternative models of electroweak symmetry breaking
Flavour physics beyond the SM
Computational algorithms and tools...etc.