论文标题
Schwarzschild和Rn黑洞的宝石嵌入在Painlevé-Gullstrand SpaceTimes
GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes
论文作者
论文摘要
利用较高的全球嵌入Minkowski时空（GEMS），我们嵌入（3+1） - 维度的Schwarzschild和Reissner-Nordström（RN）黑洞由Painlevé-Gullstrand（pg）的空间撰写，具有偏高的成分，具有偏离型的成分（5+1+1+1+1+1+1+1+1+1（5+1） 分别。结果，我们显示了空间嵌入的宝石与对角线和非对角线的等效性。此外，借助其在平坦的空间中满足各种边界条件的地球方程，我们直接获得自由下降的温度。我们还表明，在PG空间中自由降低的温度在事件视野之外明确定义，而它们等同于鹰温度，这些温度是在地平线和无穷大之间的原始弯曲范围内获得的。这些将有助于研究更现实的Kerr或旋转BTZ黑洞的宝石嵌入。
Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3+1)-dimensional Schwarzschild and Reissner-Nordström (RN) black holes written by the Painlevé-Gullstrand (PG) spacetimes, which have off-diagonal components in metrics, into (5+1)- and (5+2)-dimensional flat ones, respectively. As a result, we have shown the equivalence of the GEMS embeddings of the spacetimes with the diagonal and off-diagonal terms in metrics. Moreover, with the aid of their geodesic equations satisfying various boundary conditions in the flat embedded spacetimes, we directly obtain freely falling temperatures. We also show that freely falling temperatures in the PG spacetimes are well-defined beyond the event horizons, while they are equivalent to the Hawking temperatures, which are obtained in the original curved ones in the ranges between the horizon and the infinity. These will be helpful to study GEMS embeddings of more realistic Kerr, or rotating BTZ black holes.
