Minkowski spacetime

Minkowski metric describes an empty flat spacetime. Diagrams of the Minkowski spacetime are shown for comparison with black hole spacetimes.

Three-dimensional compactified diagrams represent the whole Minkowski spacetime including "points at the infinity". A pair of uniformly accelerated observers moving along a common line in oposite directions is also shown. Both observers enter the spacetime with the velocity of light through the conformal infinity, they move toward each other until they stop and start to move away from each other back to the infinity.

Only the angular coordinate φ around the axis of motion is suppressed in the three-dimensional diagrams. A rotation around this axis is a symmetry of the spacetime.

The outer boundary of the diagrams corresponds to the conformal infinity. The worldlines of the observers are drawn in red. Blue surfaces indicate the acceleration horizon causally separating both observers. It is a null surface and thus it is only one way traversable for a physical observer. Finally, the worldline of the origin between both observers is also shown.

Standard radial two-dimensional conformal diagrams and their embedding into the three-dimensiona diagram is also shown.


Interactive diagrams needs a browser supporting Java applets. It uses LiveGraphics3D by Martin Kraus. It can take some time to download and to initiate these diagrams.
© 2005-12-31; Pavel Krtouš <Pavel.Krtous@mff.cuni.cz>