{"title":"受最小不确定性方法启发的黑洞奇点的半经典解决方法","authors":"Brayan Melchor , Rolando Perca , Wilfredo Yupanqui","doi":"10.1016/j.nuclphysb.2024.116584","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a new lapse function that simplifies the Hamiltonian constraint, describing the interior of the black hole in terms of the Ashtekar-Barbero variables, into a more straightforward form. The new Hamiltonian leads to different equations of motion than those found in the literature, but through a suitable transformation between temporal parameters, it is found that such a choice leads us to the classical solutions of the Schwarzschild metric, still preserving the physical singularity. In order to resolve this singularity, and inspired by the minimal uncertainty approach, we modify the classical algebra between the dynamic variables of the model, imposing an effective dynamics within the black hole. As a consequence, one of the dynamic variables, denoted by <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span>, acquires a minimum value at the singularity <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span>, and on the other hand, the variable related to the radius of the 2-sphere, <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>, leads to the resolution of the classical singularity of the black hole by replacing it with a bounce that connects the interior of the black hole with the interior of the white hole. This bounce occurs in the Planck-scale region, where a new event horizon manifests. Upon crossing this horizon, the nature of the interval changes from spatial to temporal outside the white hole.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324001500/pdfft?md5=1064a44684aaad59f211cb5906948e5a&pid=1-s2.0-S0550321324001500-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach\",\"authors\":\"Brayan Melchor , Rolando Perca , Wilfredo Yupanqui\",\"doi\":\"10.1016/j.nuclphysb.2024.116584\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose a new lapse function that simplifies the Hamiltonian constraint, describing the interior of the black hole in terms of the Ashtekar-Barbero variables, into a more straightforward form. The new Hamiltonian leads to different equations of motion than those found in the literature, but through a suitable transformation between temporal parameters, it is found that such a choice leads us to the classical solutions of the Schwarzschild metric, still preserving the physical singularity. In order to resolve this singularity, and inspired by the minimal uncertainty approach, we modify the classical algebra between the dynamic variables of the model, imposing an effective dynamics within the black hole. As a consequence, one of the dynamic variables, denoted by <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span>, acquires a minimum value at the singularity <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span>, and on the other hand, the variable related to the radius of the 2-sphere, <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>, leads to the resolution of the classical singularity of the black hole by replacing it with a bounce that connects the interior of the black hole with the interior of the white hole. This bounce occurs in the Planck-scale region, where a new event horizon manifests. Upon crossing this horizon, the nature of the interval changes from spatial to temporal outside the white hole.</p></div>\",\"PeriodicalId\":54712,\"journal\":{\"name\":\"Nuclear Physics B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-06-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0550321324001500/pdfft?md5=1064a44684aaad59f211cb5906948e5a&pid=1-s2.0-S0550321324001500-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nuclear Physics B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0550321324001500\",\"RegionNum\":3,\"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":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324001500","RegionNum":3,"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}
引用次数: 0
摘要
我们提出了一种新的失效函数,它将用阿什特卡-巴贝罗变量描述黑洞内部的哈密顿约束简化为一种更直接的形式。新的汉密尔顿导致了与文献中不同的运动方程,但通过时间参数之间的适当变换,我们发现这样的选择会引导我们找到施瓦兹柴尔德度量的经典解,同时仍然保留了物理奇点。为了解决这个奇点,受最小不确定性方法的启发,我们修改了模型动态变量之间的经典代数,在黑洞内部施加了一个有效的动力学。因此,其中一个动态变量(用 pb 表示)在奇点 t=0 时获得了最小值,而另一方面,与 2 球半径有关的变量 pc 则导致了黑洞经典奇点的解决,用连接黑洞内部和白洞内部的反弹取代了经典奇点。这种反弹发生在普朗克尺度区域,在那里会出现一个新的事件视界。穿过这个视界后,白洞外的时间间隔性质就会从空间性转变为时间性。
Semiclassical resolution of the black hole singularity inspired in the minimal uncertainty approach
We propose a new lapse function that simplifies the Hamiltonian constraint, describing the interior of the black hole in terms of the Ashtekar-Barbero variables, into a more straightforward form. The new Hamiltonian leads to different equations of motion than those found in the literature, but through a suitable transformation between temporal parameters, it is found that such a choice leads us to the classical solutions of the Schwarzschild metric, still preserving the physical singularity. In order to resolve this singularity, and inspired by the minimal uncertainty approach, we modify the classical algebra between the dynamic variables of the model, imposing an effective dynamics within the black hole. As a consequence, one of the dynamic variables, denoted by , acquires a minimum value at the singularity , and on the other hand, the variable related to the radius of the 2-sphere, , leads to the resolution of the classical singularity of the black hole by replacing it with a bounce that connects the interior of the black hole with the interior of the white hole. This bounce occurs in the Planck-scale region, where a new event horizon manifests. Upon crossing this horizon, the nature of the interval changes from spatial to temporal outside the white hole.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.