Speaker
Pavlina Jaluvkova
(JINR Dubna, Russia;Silesian university in Opava, Czech Republic)
Description
In this work, we propose the way to construct the model of the cosmological black hole in the dust-filled universe on the basis of the exact solution to the Einstein equations of the Lemaitre-Tolman-Bondi class. We have found such solution as a particular case of Tolman solution with the arbitrary functions chosen in a special way such that the solution includes both the Schwarzschild and Friedmann solutions as its natural limiting cases. We have analyzed the properties of the obtained solution for the three types of spatial curvature and built the R-T-structure of the resulting spacetime, showing the horizons and singularities of the solution. We have demonstrated that in the center of symmetry of the obtained spacetime there is a region where the black hole is situated. The question of avoiding the shell-crossing in the model was solved. The trajectories of the test particles were built near the black hole for both comoving and distant observer. Although the metric for the distant observer was non-static, we have obtained the physically realistic picture of motion of the test particles around the black hole. From our analysis it follows that within the second order accuracy one will obtain the usual results, but cosmological corrections will appear in the next order. And as far as the obtained solution is exact the cosmological corrections to the Schwarzschild asymptotic may be found analytically up to any order of accuracy.
