**Publication date:** Nov 2006

**Abstract:**

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.

**Authors:**

Hledík, Stanislav; Stuchlík, Zdeněk; Cipko, Alois;