Embedding diagrams for the Reissner-Nordström spacetime (Q1878352)

Embedding of a curved surface in the Euclidean space visually demonstrates the ``curvedness'' or curvature of the surface. Embedding diagrams therefore become excellent tools for visualizing the curvature of spacetime; i.e. the gravitational field. The particle trajectories could easily be seen and they would be analogues of the field lines in electromagnetic theory -- they are indeed field lines of the gravitational field. One of the most interesting objects in this context is the black hole causing critical warping of space around it so that no null ray can propagate out of it. The embedding diagram makes this phenomenon transparent and visually illuminating. The main aim of this note is for the Reissner-Nordström black hole to relate the scalar curvature of the surface being embedded with the character of the embedding diagram. The \(r-t\) and \(r-\phi\) 2-surfaces are embedded into \((2 +1)/3\)-Euclidean space and the relation between the diagrams and the corresponding scalar curvature of the 2-metrics is discussed.