标题： 静态和动态布兰斯-迪克球对称模型的不变描述 显示英文标题

标题： Invariant description of static and dynamical Brans-Dicke spherically symmetric models

摘要： 我们使用不变量研究球对称静态和动态Brans-Dicke理论的精确解，特别是利用Cartan标量的Newman Penrose形式主义。 这些解的GR极限通过Cartan不变量的使用以及Cartan-Karlhede算法进行检验，并且还通过标量多项式不变量的分析得到进一步支持。 确定这些时空中的视界出现主要取决于解族的一个参数$n$。 特别是，出现了无膨胀表面，对于参数值的子集，这些表面定义了与之前工作中识别的标准表面（例如，有效视界）不同的额外表面。 在静态球对称Brans-Dicke解中，这些表面之前已被证明在两种理论之间存在适当极限时对应于广义相对论中的Schwarzschild视界。 我们还表明，对于这些情况，存在其他几何定义的视界，并确定了对应广义相对论极限不是Schwarzschild但仍然包含视界的全部解。 其中一些其他表面的识别在以前的工作中有所提及，并在此工作中以不变方式表征。 在动态Brans-Dicke解族的情况下，我们识别了与静态情况类似不变定义的表面，并给出了它们几何结构的不变表征。 通过分析Cartan不变量，我们通过使用Cartan-Karlhede算法确定了这些解族中哪些成员是局部等价的。 此外，我们利用Cartan不变量识别了黑洞表面、裸奇点和虫洞。 本工作的目的是展示Cartan不变量在描述精确解性质方面的有用性。 显示英文摘要

摘要： We investigate spherically symmetric static and dynamical Brans-Dicke theory exact solutions using invariants and, in particular, the Newman Penrose formalism utilizing Cartan scalars. The GR limit of these solutions is examined through the use of Cartan invariants via the Cartan-Karlhede algorithm and is additionally supported by analysis of scalar polynomial invariants. It is determined that the appearance of horizons in these spacetimes depends primarily on one of the parameters, $n$, of the family of solutions. In particular, expansion-free surfaces appear which, for a subset of parameter values, define additional surfaces distinct from the standard surfaces (e.g., apparent horizons) identified in previous work. These surfaces in static spherically symmetric Brans-Dicke solutions was previously shown to correspond to the Schwarzschild horizon in general relativity when an appropriate limit exists between the two theories. We show additionally that other geometrically defined horizons exist for these cases, and identify all solutions for which the corresponding general relativity limit is not a Schwarzschild one, yet still contains horizons. The identification of some of these other surfaces was noted in previous work and is characterized invariantly in this work. In the case of the family of dynamical Brans-Dicke solutions, we identify similar invariantly defined surfaces as in the static case and present an invariant characterization of their geometries. Through the analysis of the Cartan invariants, we determine which members of these families of solutions are locally equivalent, through the use of the Cartan-Karlhede algorithm. In addition, we identify black hole surfaces, naked singularities, and wormholes with the Cartan invariants. The aim of this work is to demonstrate the usefulness of Cartan invariants for describing properties of exact solutions.