论文标题
将外部重力场与轴向对称物体的能量动量张量连接起来
Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
论文作者
论文摘要
在Hernandez-Pastora等人中开发了一种适当匹配Weyl家族的任何真空溶液的内部轴向对称指标的方法。 （类量子重力33：235005，2016）。对于某些真空溶液的情况，表明内部度量的最简单解决方案导致具有良好行为良好的能量条件的来源。现在，我们整合了场等方程，以根据源代码和压力来获得内部度量函数。同样，计算了这些全局模型的状态兼容状态方程。描述源的内部度量和合适的能量动量张量是根据外部度量函数构建的。在紧凑型物体的边界上，由能量动量张量定义的压力TM的行为与外部重力场有关。这一事实使我们能够探索当删除全局度量的球形对称时在物质分布上产生的差异。最后，获得了从匹配条件得出的方程式，使我们能够计算出外部摩术作为源积分的Weyl系数。因此，可以用源的物质分布来表达全局模型的相对论多极成分。
A method to construct interior axially symmetric metrics that appropriately match with any vacuum solution of the Weyl family is developed in Hernandez-Pastora etal. (Class Quantum Gravity 33:235005, 2016). It was shown,for the case of some vacuum solutions, that the simplestsolution for the interior metric leads to sources with well behaved energy conditions. Now, we integrate the field equa-tions to obtain the interior metric functions in terms of theanisotropies and pressures of the source. As well, the compatible equations of state for these global models are calculated. The interior metric and the suitable energy momentum tensor describing the source are constructed in terms of the exterior metric functions. At the boundary of the compact object,the behaviour of a pressure Tm, defined from the energy momentum tensor, is shown to be related with the exterior gravitational field. This fact allows us to explore the differences arising at the matter distribution when the sphericalsymmetry of the global metric is dropped. Finally, an equation derived from the matching conditions is obtained whichallows us to calculate the Weyl coefficients of the exteriormetric as source integrals. Hence the Relativistic MultipoleMoments of the global model can be expressed in terms ofthe matter distribution of the source.
