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arXiv 1702.01754gr-qchep-th
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静态球对称解的整体结构

Global structure of static spherically symmetric solutions surrounded by quintessence

Miguel Cruz, Apratim Ganguly, Radouane Gannouji, Genly Leon, Emmanuel N. Saridakis

摘要:

我们研究所有静态球对称解的背景下,广义相对论包围的最小耦合quintessence字段,使用动力系统分析。应用1+1+2形式并引入适当的高斯曲率的归一化变量,我们能够将场方程重新表示为一阶微分方程。在无质量正则标量场的情况下,我们恢复了所有已知的黑洞结果,如Fisher解,我们发现,除了史瓦西解,所有其他的解决方案是裸奇点。此外,我们确定了对称相空间,对应于白洞部分的解决方案,并在幻影场的情况下,我们能够提取虫洞存在的条件,并定义所有可能的类的解决方案,如冷黑洞,奇异时空和虫洞,如埃利斯虫洞,例如。对于指数势,我们发现渐近平坦的黑洞解是唯一的,它是Schwarzschild时空,而所有其他的解都是裸奇点。此外,我们发现的解决方案连接到一个白洞通过最大半径,而不是一个最小半径(喉),如虫洞的解决方案,因此违反耀斑的条件。最后,我们找到了一个渐近AdS时空的势形式的充分必要条件,以及渐近平坦黑洞存在的必要条件。

英文摘要:

We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible class of solutions such as Cold Black holes, singular spacetimes and wormholes like Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

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