爱因斯坦静态宇宙的天体物理学窥视
An astrophysical peek into Einstein's static universe
摘要：
我们在这里直接从爱因斯坦方程导出爱因斯坦静态宇宙（ESU）的度规，即，通过同时考虑$G_{ik}$和$T_{ik}$。我们发现，为了使流体的压力和加速度是{ \em均匀}和有限的，尽管存在一个坐标奇异性，有效密度$ρ_e = ρ+ Λ/8 π=0$，其中$Λ$是宇宙学常数。在弱能量条件下，这将意味着ESU的$ρ= Λ=0$。这意味着，如果需要在某个模型中调用"排斥引力“的来源，（i）该模型必须是非静态的，（ii）排斥性引力必须是由于具有负压的“精粹”或“暗能量”流体，并出现在右手边（RHS）通过$T_{ij}$而不是通过驻留在同一方程的LHS上的基本常数，正常物质和"暗能量流体“的能量密度应该是时间依赖性的。事实上，排斥引力是由于与时间无关的$Λ$，很难理解为什么相关的能量密度应该比量子引力预测的值低大约$10^{120}$倍。另一方面，对于能量密度与时间相关的暗能量流体来说，理解如此极低的当前能量密度会容易得多：流体能量密度的原始初始值可能等于量子引力值，而当前的低值是由于随时间衰减而产生的。
英文摘要：
We derive here the metric for Einstein's static universe (ESU) directly from Einstein equation, i.e., by considering both $G_{ik}$ and $T_{ik}$. We find that in order that the fluid pressure and acceleration are {\em uniform} and finite despite the presence of a coordinate singularity, the effective density $ρ_e = ρ+ Λ/8 π=0$, where $Λ$ is the cosmological constant. Under weak energy condition, this would imply $ρ= Λ=0$ for ESU. This means that if one would need to invoke a source of ``repulsive gravity'' in some model, (i) the model must be non-static, (ii) the repulsive gravity must be due to a ``quintessence'' or a ``dark energy'' fluid with negative pressure and appear on the right hand side (RHS) of the Einstein equation through $T_{ij}$ rather than through a fundamental constant residing on the LHS of the same equation, and (iii) energy density of both normal matter and the ``dark energy fluid'' should be time dependent. In fact, the repulsive gravity would be due to a time independent $Λ$, it would be extremely difficult to understand why the associated energy density should be approximately $10^{120}$ times lower than the value predicted by quantum gravity. On the other hand, for a dark energy fluid whose energy density is time dependent, it would be much easier to understand such an extremely low present energy density: the original initial value of the energy density of the fluid could be equal to the quantum gravity value while the present low value is due to decay with time.
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