论文标题
在米尔恩样空位的渐近假设上
On the asymptotic assumptions for Milne-like spacetimes
论文作者
论文摘要
像米尔恩（Milne）一样的空位是一类双曲线FLRW空间，可以通过大爆炸的连续时空扩展，$τ= 0 $。扩展的存在是从共形的Minkowskian坐标中编写度量标准的，并假设比例因子满足$ a（τ）=τ+ o（τ^{1+ \ varepsilon}）$作为$ \ varepsilon> 0 $ 0 $。这个渐近假设意味着$ a（τ）=τ+ o（τ）$。在本文中，我们表明$ a（τ）=τ+ o（τ）$不足以通过$τ= 0 $实现扩展名，但是只要其衍生产品收敛为$τ\ \ 0 $。我们还表明，$ \ varepsilon $ in $ a（τ）=τ+ o（τ^{1+ \ varepsilon}）$无需通过$τ= 0 $实现扩展。
Milne-like spacetimes are a class of hyperbolic FLRW spacetimes which admit continuous spacetime extensions through the big bang, $τ= 0$. The existence of the extension follows from writing the metric in conformal Minkowskian coordinates and assuming that the scale factor satisfies $a(τ) = τ+ o(τ^{1+\varepsilon})$ as $τ\to 0$ for some $\varepsilon > 0$. This asymptotic assumption implies $a(τ) = τ+ o(τ)$. In this paper, we show that $a(τ) = τ+ o(τ)$ is not sufficient to achieve an extension through $τ= 0$, but it is necessary provided its derivative converges as $τ\to 0$. We also show that the $\varepsilon$ in $a(τ) = τ+ o(τ^{1+\varepsilon})$ is not necessary to achieve an extension through $τ= 0$.
