{"title":"三阶拉夫洛克引力下弦云中的林德勒轨迹","authors":"M. Umair Shahzad, Aneela Sadaf","doi":"10.1007/s10714-024-03200-4","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the Rindler trajectories in the Cloud of strings in 3rd-order Lovelock gravity. According to the generalization of the Letaw–Frenet equations for curved spacetime (ST), the trajectory will continue to accelerate linearly and uniformly throughout its motion. The ST of the Cloud of strings in 3rd-order Lovelock gravity, a boundary is established on the bound of the accelerated magnitude |<i>a</i>| for radially inward traveling trajectories in the expression of the BH mass <i>m</i> which is represented by <span>\\(|a|\\le {\\frac{ \\left( b+1 \\right) ^{3/2}}{3 \\sqrt{3} m}}\\)</span>. For a certain selection of asymptotic initial data <i>h</i>, the linearly uniformly accelerated trajectory always enters the BH for acceleration |<i>a</i>| greater than the bound value. To study the bound value by |<i>a</i>|, the radial linearly uniformly accelerated trajectory can only travel to infinity within a small radius or the distance of the closest approach. However, it is observed that when the bound <span>\\(|a| = {\\frac{ \\left( b+1 \\right) ^{3/2}}{3 \\sqrt{3} m}}\\)</span> is saturated, and this distance approaches its lowest value of <span>\\(r_b = {\\frac{3m}{b+1}}\\)</span>. We also demonstrate that the value of the acceleration has a limited constraint, there is always an extension of the closest approach <span>\\(r_b > {\\frac{2m}{b+1}}\\)</span> for <span>\\(|a|\\le B(m, h)\\)</span>, for each set of finite asymptotic initial data <i>h</i>.\n</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rindler trajectories in cloud of strings in 3rd order Lovelock gravity\",\"authors\":\"M. Umair Shahzad, Aneela Sadaf\",\"doi\":\"10.1007/s10714-024-03200-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper studies the Rindler trajectories in the Cloud of strings in 3rd-order Lovelock gravity. According to the generalization of the Letaw–Frenet equations for curved spacetime (ST), the trajectory will continue to accelerate linearly and uniformly throughout its motion. The ST of the Cloud of strings in 3rd-order Lovelock gravity, a boundary is established on the bound of the accelerated magnitude |<i>a</i>| for radially inward traveling trajectories in the expression of the BH mass <i>m</i> which is represented by <span>\\\\(|a|\\\\le {\\\\frac{ \\\\left( b+1 \\\\right) ^{3/2}}{3 \\\\sqrt{3} m}}\\\\)</span>. For a certain selection of asymptotic initial data <i>h</i>, the linearly uniformly accelerated trajectory always enters the BH for acceleration |<i>a</i>| greater than the bound value. To study the bound value by |<i>a</i>|, the radial linearly uniformly accelerated trajectory can only travel to infinity within a small radius or the distance of the closest approach. However, it is observed that when the bound <span>\\\\(|a| = {\\\\frac{ \\\\left( b+1 \\\\right) ^{3/2}}{3 \\\\sqrt{3} m}}\\\\)</span> is saturated, and this distance approaches its lowest value of <span>\\\\(r_b = {\\\\frac{3m}{b+1}}\\\\)</span>. We also demonstrate that the value of the acceleration has a limited constraint, there is always an extension of the closest approach <span>\\\\(r_b > {\\\\frac{2m}{b+1}}\\\\)</span> for <span>\\\\(|a|\\\\le B(m, h)\\\\)</span>, for each set of finite asymptotic initial data <i>h</i>.\\n</p></div>\",\"PeriodicalId\":578,\"journal\":{\"name\":\"General Relativity and Gravitation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-02-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"General Relativity and Gravitation\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10714-024-03200-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-024-03200-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Rindler trajectories in cloud of strings in 3rd order Lovelock gravity
This paper studies the Rindler trajectories in the Cloud of strings in 3rd-order Lovelock gravity. According to the generalization of the Letaw–Frenet equations for curved spacetime (ST), the trajectory will continue to accelerate linearly and uniformly throughout its motion. The ST of the Cloud of strings in 3rd-order Lovelock gravity, a boundary is established on the bound of the accelerated magnitude |a| for radially inward traveling trajectories in the expression of the BH mass m which is represented by \(|a|\le {\frac{ \left( b+1 \right) ^{3/2}}{3 \sqrt{3} m}}\). For a certain selection of asymptotic initial data h, the linearly uniformly accelerated trajectory always enters the BH for acceleration |a| greater than the bound value. To study the bound value by |a|, the radial linearly uniformly accelerated trajectory can only travel to infinity within a small radius or the distance of the closest approach. However, it is observed that when the bound \(|a| = {\frac{ \left( b+1 \right) ^{3/2}}{3 \sqrt{3} m}}\) is saturated, and this distance approaches its lowest value of \(r_b = {\frac{3m}{b+1}}\). We also demonstrate that the value of the acceleration has a limited constraint, there is always an extension of the closest approach \(r_b > {\frac{2m}{b+1}}\) for \(|a|\le B(m, h)\), for each set of finite asymptotic initial data h.
期刊介绍:
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.