Orodruin

The Lorentz invariant hyper surfaces are by definition hyperboloids of the form (ct)^2 - x^2 - y^2 - z^2 = constant. Light cones are a special case of this where the constant is zero. The hyperboloids have a special role as they may represent, for example, the mass-shell of a particle/object. Furthermore, hyperbola such as (ct)^2 - x^2 = -k^2, y = z = 0, represent world-lines of observers with constant proper acceleration and their shape is also invariant under Lorentz transformations.