Farzan Mushtaq , Xia Tiecheng , Allah Ditta , Waheed Al-Masry , Ateyah A. Al-Zahrani , Shahid M. Ramay , Asif Mahmood
{"title":"通过弱引力等离子体透镜探测弗罗洛夫黑洞","authors":"Farzan Mushtaq , Xia Tiecheng , Allah Ditta , Waheed Al-Masry , Ateyah A. Al-Zahrani , Shahid M. Ramay , Asif Mahmood","doi":"10.1016/j.dark.2025.102094","DOIUrl":null,"url":null,"abstract":"<div><div>This study investigates the properties of the weak gravitational lensing by using the Gauss–Bonnet theorem in the context of the Frolov black hole. By employing the Gauss–Bonnet theorem, we determine the deflection angle of the black hole for spherically balanced space–time and derive the Gaussian optical curvature. The resulting light deflection angle at the weak field limits demonstrates that light bending is a topological and universal process. Additionally, we determine the light’s deflection angle within the plasma medium’s framework. Furthermore, under the impact of plasma medium and for non-plasma medium, the behaviour of the deflection angle is demonstrated explicitly by the black hole. This research also investigates the related properties of particle dynamics including, effective force and the Lyapunov component. Hence, greater deflection angle depicts the greater photon frequency. Thus, increase in parameters <span><math><mrow><mi>η</mi><mo>,</mo><mspace></mspace><mi>q</mi><mo>,</mo><mspace></mspace><mi>a</mi></mrow></math></span> forecasts decrease in photon frequency and increase in <span><math><mi>α</mi></math></span> and plasma medium <span><math><mi>N</mi></math></span> suggests increase photon frequency. Lyapunov exponent indicates suggests the stability of the black hole solution. In terms of effective force parameters <span><math><mi>η</mi></math></span>, <span><math><mi>q</mi></math></span> and <span><math><mi>a</mi></math></span> suggests weak attraction of the particle whereas parameters <span><math><mi>α</mi></math></span> suggests strong attractions.</div></div>","PeriodicalId":48774,"journal":{"name":"Physics of the Dark Universe","volume":"50 ","pages":"Article 102094"},"PeriodicalIF":6.4000,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Probing the Frolov black hole via weak gravitational plasma lensing\",\"authors\":\"Farzan Mushtaq , Xia Tiecheng , Allah Ditta , Waheed Al-Masry , Ateyah A. Al-Zahrani , Shahid M. Ramay , Asif Mahmood\",\"doi\":\"10.1016/j.dark.2025.102094\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This study investigates the properties of the weak gravitational lensing by using the Gauss–Bonnet theorem in the context of the Frolov black hole. By employing the Gauss–Bonnet theorem, we determine the deflection angle of the black hole for spherically balanced space–time and derive the Gaussian optical curvature. The resulting light deflection angle at the weak field limits demonstrates that light bending is a topological and universal process. Additionally, we determine the light’s deflection angle within the plasma medium’s framework. Furthermore, under the impact of plasma medium and for non-plasma medium, the behaviour of the deflection angle is demonstrated explicitly by the black hole. This research also investigates the related properties of particle dynamics including, effective force and the Lyapunov component. Hence, greater deflection angle depicts the greater photon frequency. Thus, increase in parameters <span><math><mrow><mi>η</mi><mo>,</mo><mspace></mspace><mi>q</mi><mo>,</mo><mspace></mspace><mi>a</mi></mrow></math></span> forecasts decrease in photon frequency and increase in <span><math><mi>α</mi></math></span> and plasma medium <span><math><mi>N</mi></math></span> suggests increase photon frequency. Lyapunov exponent indicates suggests the stability of the black hole solution. In terms of effective force parameters <span><math><mi>η</mi></math></span>, <span><math><mi>q</mi></math></span> and <span><math><mi>a</mi></math></span> suggests weak attraction of the particle whereas parameters <span><math><mi>α</mi></math></span> suggests strong attractions.</div></div>\",\"PeriodicalId\":48774,\"journal\":{\"name\":\"Physics of the Dark Universe\",\"volume\":\"50 \",\"pages\":\"Article 102094\"},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2025-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physics of the Dark Universe\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2212686425002870\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of the Dark Universe","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2212686425002870","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Probing the Frolov black hole via weak gravitational plasma lensing
This study investigates the properties of the weak gravitational lensing by using the Gauss–Bonnet theorem in the context of the Frolov black hole. By employing the Gauss–Bonnet theorem, we determine the deflection angle of the black hole for spherically balanced space–time and derive the Gaussian optical curvature. The resulting light deflection angle at the weak field limits demonstrates that light bending is a topological and universal process. Additionally, we determine the light’s deflection angle within the plasma medium’s framework. Furthermore, under the impact of plasma medium and for non-plasma medium, the behaviour of the deflection angle is demonstrated explicitly by the black hole. This research also investigates the related properties of particle dynamics including, effective force and the Lyapunov component. Hence, greater deflection angle depicts the greater photon frequency. Thus, increase in parameters forecasts decrease in photon frequency and increase in and plasma medium suggests increase photon frequency. Lyapunov exponent indicates suggests the stability of the black hole solution. In terms of effective force parameters , and suggests weak attraction of the particle whereas parameters suggests strong attractions.
期刊介绍:
Physics of the Dark Universe is an innovative online-only journal that offers rapid publication of peer-reviewed, original research articles considered of high scientific impact.
The journal is focused on the understanding of Dark Matter, Dark Energy, Early Universe, gravitational waves and neutrinos, covering all theoretical, experimental and phenomenological aspects.