论文标题
Schwarzschild公制的最大扩展：从Painlevé-Gullstrand到Kruskal-Szekeres
Maximal extension of the Schwarzschild metric: From Painlevé-Gullstrand to Kruskal-Szekeres
论文作者
论文摘要
我们找到一个特定的坐标系，该系统从Painlevé-Gullstrand的部分延伸到Kruskal-Szekeres最大扩展，因此在统一图片中表现出Schwarzschild指标的最大扩展。我们通过采用两次坐标来做到这一点，其中一个是适当的及时的测量学的一致性，另一个是适当的时间，是摄入及时的地球测量学的一致性，两者都以每单位质量$ e $相同的能量进行参数。 $ e $在$ 1 \ 1 \ leq e <\ infty $带有限制$ e = \ infty $的范围内产生Kruskal-Szekeres最大扩展。因此，通过这样的集成描述，人们看到了Kruskal-Szekeres解决方案属于由$ e $参数化的扩展家族。我们的扩展家族与Novikov-Lemaître家族不同，这也是通过及时的地球级的能量$ e $ e $的参数，novikov的扩展价格为$ 0 <e <1 $，并且是最大的，并且以$ 1 \ leq e <\ iftty $ limimim and limimim and nockimal和mike noffty usevers novimal and theLemaîtreteExtenshing持有。时空而不是在Kruskal-Szekeres时空结束。
We find a specific coordinate system that goes from the Painlevé-Gullstrand partial extension to the Kruskal-Szekeres maximal extension and thus exhibit the maximal extension of the Schwarzschild metric in a unified picture. We do this by adopting two time coordinates, one being the proper time of a congruence of outgoing timelike geodesics, the other being the proper time of a congruence of ingoing timelike geodesics, both parameterized by the same energy per unit mass $E$. $E$ is in the range $1\leq E<\infty$ with the limit $E=\infty$ yielding the Kruskal-Szekeres maximal extension. So, through such an integrated description one sees that the Kruskal-Szekeres solution belongs to this family of extensions parameterized by $E$. Our family of extensions is different from the Novikov-Lemaître family parameterized also by the energy $E$ of timelike geodesics, with the Novikov extension holding for $0<E<1$ and being maximal, and the Lemaître extension holding for $1\leq E<\infty$ and being partial, not maximal, and moreover its $E=\infty$ limit evanescing in a Minkowski spacetime rather than ending in the Kruskal-Szekeres spacetime.
