非静态膜世界恒星的静态外部
Static exteriors for nonstatic braneworld stars
摘要：
我们研究了在兰德尔$&$ Sundrum II型膜世界场景中非静态球对称恒星可能的静态非史瓦西外部。因此，恒星表面外的真空区被假定为方程$^{(4)}R = 0$的静态解，其中$^{(4)}R $是具有球对称性的四维Ricci张量的标量曲率。首先，我们表明，非静态领域的标准匹配条件是更严格的比静态的，他们导致一个特定的要求真空区域以外的非静态恒星，这是缺席的情况下静态恒星。其次，在不对星体内部的物质介质做任何假设的情况下，我们在膜上证明了以下定理：对于{ \it any}非静态球形星体，没有旋转，只有两种可能的静态外部;它们是史瓦西外部和“Reissner-Nordstr{<$} m-like”外部。这与流体静力平衡中的恒星的情况截然不同，流体静力平衡中的恒星有一个更大的非史瓦西静态外部族。
英文摘要：
We study possible static non-Schwarzschild exteriors for nonstatic spherically symmetric stars in a Randall $&$ Sundrum type II braneworld scenario. Thus, the vacuum region outside the surface of a star is assumed to be a static solution to the equation $^{(4)}R = 0$, where $^{(4)}R $ is the scalar curvature of the 4-dimensional Ricci tensor with spherical symmetry. Firstly, we show that for nonstatic spheres the standard matching conditions are much more restrictive than for static ones; they lead to a specific requirement on the vacuum region outside of a nonstatic star, that is absent in the case of static stars. Secondly, without making any assumption about the bulk, or the material medium inside the star, we prove the following theorem on the brane: for {\it any} nonstatic spherical star, without rotation, there are only two possible static exteriors; these are the Schwarzschild and the "Reissner-Nordstr{ö}m-like" exteriors. This is quite distinct from the case of stars in hydrostatic equilibrium which admit a much larger family of non-Schwarzschild static exteriors.
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