Publication date: Nov 2006
It is hard to imagine curved spacetimes of General Relativity. A simple
but powerful way how to achieve this is visualizing them via embedding
diagrams of both ordinary geometry and optical reference geometry. They
facilitate to gain an intuitive insight into the gravitational field
rendered into a curved spacetime, and to assess the influence of
parameters like electric charge and spin of a black hole, magnetic field
or cosmological constant. Optical reference geometry and related
inertial forces and their relationship to embedding diagrams are
particularly useful for investigation of test particles motion.
Embedding diagrams of static and spherically symmetric, or stationary
and axially symmetric black-hole and naked-singularity spacetimes thus
present a useful concept for intuitive understanding of these
spacetimes‘ nature. We concentrate on general way of embedding into
3-dimensional Euclidean space, and give a set of illustrative examples.
Hledík, Stanislav; Stuchlík, Zdeněk; Cipko, Alois;