Instant displacements of particles

Instant displacements of particles are naturally permitted in the space-time of the General Theory of Relativity. Teleportation of substantial particles and photons realizes itself in different space-time regions. However, it would be a mistake to think that teleportation requires acceleration of a substantial particle to super-light speeds (the tachyon region), while a photon needs to be accelerated to infinite speed. If gravitational potential is essential and the space rotates at a speed close to light velocity, substantial particles may be teleported. Photons can reach the teleportation condition easier, because they move at light velocity. From the viewpoint of a regular observer, as soon as the teleportation condition is realized in the neighborhood around a moving particle, such a particle ``disappears'' although it continues its motion at a sub-light coordinate velocity u$^{\mathrm{i}}$(or at the velocity of light) in another space-time region invisible for us. Then, having its velocity reduced, or if something else disrupts the teleportation condition (reduction of gravitational potential or the space rotation speed), it ``appears'' at the same observable moment at another point of our observable space at that distance and in that direction of its u$^{\mathrm{i}}$.