Dynamical black hole in a bouncing universe

Abstract

We analyze the causal structure of McVittie spacetime for a classical bouncing cosmological model. In particular, we compute the trapping horizons of the metric and integrate the trajectories of radial null geodesics before, during, and after the bounce takes place. In the contracting phase up to the occurrence of the bounce, a dynamical black hole is present. When the universe reaches a certain minimum scale, the trapping horizons disappear and the black hole ceases to exist. After the bounce, the central weak singularity becomes naked. In the expanding phase, for large positive values of the cosmic time, the behaviour of null geodesics indicates that the solution contains a black hole. These results suggest that neither a contracting nor an expanding universe can accommodate a black hole at all times.

Dissimilar donuts in the sky? Effects of a pressure singularity on the circular photon orbits and shadow of a cosmological black hole

“…It is undoubtable at present day that the McVittie metric describes a black hole in a dynamically expanding FRW Universe [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The McVittie spacetime metric for a flat FRW background in geometrized units (G = c = 1), reads…”

“…The quantity χ(R, t) = f 2 − g 2 = g μν ∇ μ r∇ ν R basically defines the trapped and untrapped spacetime regions of the spherically symmetric spacetime. The condition for having circular photon orbits of radius R c for all cosmic times is [43]…”

“…In order to realize technically the above idea, we shall use the McVittie metric [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The motivation is rather simple, the expansion of the Universe at cosmological scales should somehow affect the cosmological black holes.…”

“…The shadow of a black hole is basically a dark spot in the direction of a black hole in the sky, which is viewable due to the background of other light sources nearby. The McVittie metric [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] is the most refined description for describing a black hole embedded in an expanding Friedmann-Robertson-Walker (FRW) background. For a series of articles on the McVittie metric, see refs.…”

“…For a series of articles on the McVittie metric, see refs. [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] and references therein. Although initially it was debatable whether the McVittie metric describes a black hole [35], it is now widely accepted that indeed it describes a black hole in an expanding background [36,44,45,47,48], although the accretion of matter and radiation is not allowed.…”