论文标题
Einstein-Aether模型III：共形静态指标，完美的流体和标量场
Einstein-aether models III: conformally static metrics, perfect fluid and scalar fields
论文作者
论文摘要
在爱因斯坦 - 区域理论中具有完美流体源和标量场的爱因斯坦 - 区域理论中共同静态指标的渐近性质。如果是完美的流体，则恢复了一些相对论的解决方案，例如：Minkowski时空，Kasner溶液，平坦的FLRW空间和静态轨道，具体取决于正压参数$γ$。为了在本地分析声音线附近的解决方案的行为$ v^2 =γ-1$，其中$ v $是倾斜，使用了一种新的“冲击”变量。在此线上发现了两个新的平衡点。当$ 1 <γ<2 $ $ 1 <γ<2 $时，这些点不存在。在一般相对论的限制情况下，这些点代表了用极端倾斜的刚性解决方案。在一般相对性的极限中发现了与均种载体场的因果关系变化相关的平衡点的线。对于非同质标量字段$ ϕ（t，x）$，带有潜在$ v（ϕ（t，x））$，保串静态度量的对称性限制了要考虑到$ ϕ（t，x）=ψ（x）=ψ（x）-λt，v（ϕ（t，x，x，x，x）= e^e^e^{ - 2 t} us（uct）= u（x） e^{ - \ frac {2ψ}λ} $。在某些特定情况下，提供了稳定条件的详尽分析（分析或数值）。
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime, the Kasner solution, a flat FLRW space and static orbits depending on the barotropic parameter $γ$. To analyze locally the behavior of the solutions near a sonic line $v^2=γ-1$, where $v$ is the tilt, a new "shock" variable is used. Two new equilibrium point on this line are found. These points do not exist in General Relativity when $1 <γ<2 $. In the limiting case of General Relativity these points represent stiff solutions with extreme tilt. Lines of equilibrium points associated with a change of causality of the homothetic vector field are found in the limit of General Relativity. For non-homogeneous scalar field $ϕ(t,x)$ with potential $V(ϕ(t,x))$ the symmetry of the conformally static metric restrict the scalar fields to be considered to $ ϕ(t,x)=ψ(x)-λt, V(ϕ(t,x))= e^{-2 t} U(ψ(x))$, $U(ψ)=U_0 e^{-\frac{2 ψ}λ}$. An exhaustive analysis (analytical or numerical) of the stability conditions is provided for some particular cases.
