A study of McVittie Spacetime in Stationary and Dynamical Regime

International audienceOne of the solutions of the Einstein equations, called McVittie solution, signifying a black hole embedded by the dynamic spacetime is studied. In the stationary spacetime the Mcvittie metric becomes the Schwarzschild-de Sitter metric (SdS). The geodesic of a freely falling test particle towards the black hole is examined in the SdS spacetime. It is found that unlike the Schwarzschild case the potential of such particle becomes maximum at a point where it eventually stops for a while and then resumes its motion towards the center of the black hole. It is shown that an observer or system of particles is spaghettified near the black hole singularity in the SdS spacetime. The dynamics of the universe in the framework of McVittie metric, being a generalized time dependent SdS solution, is represented in terms of that point, called stationary or turning point. The motion of the stationary point is studied in various regimes of the expanding universe and the possible outcomes are discussed in brief