论文标题
与分叉的本地化麸皮
Localizing branes with bifurcating bulks
论文作者
论文摘要
我们研究了具有嵌入式的braneworld的散装5流体进化的问题，具有平坦的braneworld。我们引入了新变量，以表达爱因斯坦方程为一个动态系统，该系统取决于状态参数$γ$和指数$λ$的方程。对于线性流体（即$λ= 1 $），我们的公式会导致方程的部分解耦，从而导致精确的解决方案。我们发现，这种流体会在值$γ= -1/2 $的值周围发展出跨临界分叉，并研究这种行为如何影响溶液的稳定性。对于非线性流体，情况更加多样化。我们发现一个$λ= 1/2 $的总体吸引子，并绘制足够的相肖像以详细展示整体动力学。我们表明，$λ= 3/2 $的值在结构上是不稳定的，并且对于其他形式的$λ$都是典型的。因此，我们观察到溶液对液体的不同“多压”形式的定性行为的明显依赖性。此外，我们证明了非线性流体的DULAC函数的存在，表示在相空间的某些子集中不可能闭合轨道。我们还提供了充分的重力溶液在Brane上定位解决方案的数值证据，以满足所有能量条件。
We study the problem of evolution of bulk 5-fluids having an embedded braneworld with a flat, de Sitter, or anti-de Sitter geometry. We introduce new variables to express the Einstein equations as a dynamical system that depends on the equation of state parameter $γ$ and exponent $λ$. For linear fluids (i.e., $λ=1$), our formulation leads to a partial decoupling of the equations and thus to an exact solution. We find that such a fluid develops a transcritical bifurcation around the value $γ=-1/2$, and study how this behaviour affects to stability of the solutions. For nonlinear fluids, the situation is more diverse. We find an overall attractor at $λ=1/2$ and draw enough phase portraits to exhibit in detail the overall dynamics. We show that the value $λ=3/2$ is structurally unstable and typical for other forms of $λ$. Consequently, we observe a noticeable dependence of the qualitative behaviour of the solutions on different `polytropic' forms of the fluid bulk. In addition, we prove the existence of a Dulac function for nonlinear fluids, signifying the impossibility of closed orbits in certain subsets of the phase space. We also provide ample numerical evidence of gravity localizing solutions on the brane which satisfy all energy conditions.
