Motion in the gravitational field of a black hole in a synchronous coordinate system

Motion of a test body, or a particle, in the gravitational field of a black hole bordering dark matter is considered. The static gravitational field of extremely compressed matter is determined by solving the Einstein and Klein- Gordon equations in the synchronous coordinate system. An extremely compressed state of matter in the form of a condensate of a quantum Bose liquid is energetically more favorable than a degenerate Fermi gas. An important difference from the Schwarzschild and Kerr black holes is the absence of a singularity in the center. In a regular gravitational field, depending on the impact parameter, there are trajectories leading through the “event horizon” into the black hole, and not just passing by. At zero temperature, depending on the pair interaction of bosons, the condensate consists of components of a superfluid and an ordinary (non-superfluid) quantum liquid. The problem of the motion of a test body inside a black hole is solved analytically in the limiting case when, against the background of dominant gravity, friction with the non-superfluid component of the Bose condensate can be neglected.