The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.

The extended space-time manifold in a uniformly accelerating reference frame is considered both for positive and negative accelerations. An analogy between the light barrier and a black hole event horizon in the theory of relativity is drawn. It is shown that bradyon-tachyon-antibradyon transformations are possible in the proper reference frame by a constant acceleration, i.e. for the light barrier penetration.

White holes (relativistic anticollapsing objects) are considered both in the five-dimensional Kaluza-Klein theory and in the many-dimensional representation of extended space-time manifolds with horizons within the framework of general relativity. In the last model white holes (e.g. Kerr-Newman) appear as anticollapsing from extra (additional) dimensions. These dimensions are connected with the global structure of space-time manifolds.

A model of gravitationally anticollapsing objects, white holes, is constructed on the basis of the Kerr metric in the limit of small rotation with a corresponding interior metric. The extended space-time manifold is considered and the spectral shift of radiation from the point of view of a remote observer is calculated for different parameters of such white holes.