论文标题
具有完美流体和标量场的爱因斯坦 - 区域模型的定性分析
Qualitative analysis of Einstein-aether models with perfect fluid and scalar fields
论文作者
论文摘要
分析了由爱因斯坦 - 安塞特理论中考虑标量场类型的物质流体或完美流体产生的微分方程溶液的空间。爱因斯坦 - 重力理论由一般相对论与单位时间类型的矢量场（称为以太）组成。在这一有效的理论中，洛伦兹不变性受到侵犯，但在矢量场的存在下保留了局部和协方差。对于模型的数学公式，使用1 + 3形式主义，允许为球形对称的非均匀度量编写字段方程，作为两个变量中偏微分方程的系统。使用均匀的对角线公式，使用公制适应同构对称性的事实，可以将部分微分方程写为普通微分方程以及代数约束。所得的方程与具有均匀性超曲面的模型非常相似。这允许使用动态系统的局部理论技术对解决方案进行定性研究。分析结果将通过数值验证。
The space of the solutions of the differential equations resulting from considering matter fluids of scalar field type or perfect fluid in Einstein-aether theory is analyzed. The Einstein-aether theory of gravity consists of General Relativity coupled to a vector field of unit time type, called the aether. In this effective theory, Lorentz invariance is violated, but locality and covariance are preserved in the presence of the vector field. For the mathematical formulation of the models, the 1 + 3 formalism is used that allows writing field equations for spherically symmetric inhomogeneous metrics as a system of partial differential equations in two variables. Using the homothetic diagonal formulation, the Partial differential equations can be written as ordinary differential equations plus algebraic constraints, using the fact that the metric adapts to homothetic symmetry. The resulting equations are very similar to those of the models with homogeneous hypersurfaces. This allows the qualitative study of the solutions using techniques of local theory of dynamic systems. Analytical results are verified numerically.
