标题： 具有五维本质的静态球对称解的整体结构 显示英文标题

标题： Global structure of static spherically symmetric solutions surrounded by quintessence

摘要： 我们研究了广义相对论背景下由最小耦合的五维场包围的所有静态球对称解，采用动力系统分析方法。 应用1+1+2形式化，并引入涉及高斯曲率的合适归一化变量后，我们成功地将场方程改写为一阶微分方程。 对于无质量规范标量场的情况，我们恢复了所有已知的黑洞结果，例如Fisher解，并发现除了施瓦西解外，其余解均为裸奇点。 此外，我们确定了与解的白洞部分相对应的对称相空间，在幻影场的情况下，我们能够提取出虫洞存在的条件，并定义了所有可能的解类，例如冷黑洞、奇异时空和像Ellis虫洞那样的虫洞。 对于指数势，我们发现渐近平坦的黑洞解是唯一的，即施瓦西时空，而其余解均为裸奇点。 此外，我们找到了通过最大半径连接到白洞的解，而不是通过最小半径（喉部）的虫洞解，因此违反了膨胀条件。 最后，我们找到了关于势的形式具有渐近AdS时空的必要且充分的条件，以及存在渐近平坦黑洞的必要条件。 显示英文摘要

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.