宇宙学、黑洞和哈勃长度以外的Shock Waves
Cosmology, Black Holes and Shock Waves Beyond the Hubble Length
摘要：
我们构造了理想流体的爱因斯坦方程的精确的、熵满足的激波解，将Oppeheimer-Snyder（OS）模型推广到非零压力的情况，{ \it在黑洞}内。这些解提出了一个新的宇宙学模型，在这个模型中，膨胀的弗里德曼-罗伯逊-沃克（FRW）宇宙从大爆炸中出现，在膨胀的前沿有一个冲击波，类似于经典的冲击波爆炸。这种爆炸的规模足以解释星系和背景辐射看起来均匀的巨大规模。在这些模型中，冲击波必须位于FRW中心的一个哈勃长度之外，这个阈值是边界，有界质量位于它自己的史瓦西半径$2M/r>1,$内，因此冲击波解在黑洞内演化。打破时间对称性的熵条件意味着冲击波必须减弱，直到它最终稳定到零压力OS界面，约束{ \em finite}总质量，从周围史瓦西时空的白洞事件视界出现。然而，与黑洞外的冲击波匹配不同，状态方程$p=\frac{c^2}{3}ρ,$（大爆炸物理学最早阶段的状态方程）在大爆炸的瞬间是{ \em区别}的--仅就这个状态方程而言，冲击波以有限的非零速度（光速）从大爆炸中出现，从那时起减速为亚光速波。这些激波解表明了一个新的宇宙学模型，在这个模型中，大爆炸起源于一个渐近平坦的史瓦西时空中的黑洞内部发生的局部爆炸。
英文摘要：
We construct exact, entropy satisfying shock wave solutions of the Einstein equations for a perfect fluid which extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\it inside the Black Hole}. These solutions put forth a new Cosmological Model in which the expanding Friedmann-Robertson-Walker (FRW) universe emerges from the Big Bang with a shock wave at the leading edge of the expansion, analogous to a classical shock wave explosion. This explosion is large enough to account for the enormous scale on which the galaxies and the background radiation appear uniform. In these models, the shock wave must lie beyond one Hubble length from the FRW center, this threshhold being the boundary across which the bounded mass lies inside its own Schwarzshild radius, $2M/r>1,$ and thus the shock wave solution evolves inside a Black Hole. The entropy condition, which breaks the time symmetry, implies that the shock wave must weaken until it eventually settles down to a zero pressure OS interface, bounding a {\em finite} total mass, that emerges from the White Hole event horizon of an ambient Schwarzschild spacetime. However, unlike shock matching outside a Black Hole, the equation of state $p=\frac{c^2}{3}ρ,$ the equation of state at the earliest stage of Big Bang physics, is {\em distinguished} at the instant of the Big Bang--for this equation of state alone, the shock wave emerges from the Big Bang at a finite nonzero speed, the speed of light, decelerating to a subluminous wave from that time onward. These shock wave solutions indicate a new cosmological model in which the Big Bang arises from a localized explosion occurring inside the Black Hole of an asymptotically flat Schwarzschild spacetime.
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