Publication date: Oct 2018
An exact solution of the Lemaître-Tolman-Bondi class is investigated as
a possible model of the Schwarzschild-like black hole embedded in a
nonstatic dust-filled universe for the three types of spatial curvature.
The solution is obtained in comoving coordinates by means of the mass
function method. It is shown that the central part of space contains a
Schwarzschild-like black hole. The R-T structure of the resulting
spacetime is built. It is shown that the solution includes both the
Schwarzschild and Friedmann solutions as its natural limits. The
geodesic equations for test particles are analyzed. The particle
observable velocities are found. The trajectories of the test particles
are built from the point of view of both comoving and distant observers.
For the distant observer, the results coincide with the Schwarzschild
picture within a second-order accuracy near the symmetry center.
Kopteva, E.; Jalůvková, P.; Bormotova, I.; Stuchlík, Z.;