Sadegh H, Kiani E, Nouri-Zonoz M
Department of Physics, University of Tehran, North Karegar Ave, Tehran, 14395-547, Iran.
Sci Rep. 2024 Aug 16;14(1):19041. doi: 10.1038/s41598-024-69871-w.
We find the spatial and dynamic embedding diagrams in stationary black hole spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms of the elliptic integrals. In other cases we obtain the spatial embedding diagrams by numerical integration of the corresponding embedding equations. These embedding diagrams are then compared through their Gaussian and mean curvatures. We also find the dynamic embedding diagrams of NUT and pure NUT spacetimes, and compare them with the dynamic embedding diagram of Schwarzschild spacetime.
我们在静态黑洞时空中找到了空间和动态嵌入图。空间嵌入包括NUT、纯NUT和克尔时空。在纯NUT时空的情况下，空间嵌入方程通过椭圆积分求解。在其他情况下，我们通过对相应嵌入方程进行数值积分来获得空间嵌入图。然后通过高斯曲率和平均曲率对这些嵌入图进行比较。我们还找到了NUT和纯NUT时空的动态嵌入图，并将它们与史瓦西时空的动态嵌入图进行比较。
