The Black Hole Universe (BHU) from a FLRW cloud
Résumé
A FLRW cloud is a solution of classical General Relativity (GR) were a homogeneous star or cloud of mass $M$ and size $R(\tau)$, is collapsing/expanding under its own gravity following a geodesic of the FLRW metric as a function of proper (comoving) time $\tau$.
This solution can be used to model the interior of a Black Hole (BH) with regular matter/radiation, without the need of negative pressure or surface terms. Our Universe could emerged from a FLRW dust cloud of $M \simeq 5 \times 10^{22} M_{\odot}$ that collapsed $\tau \simeq 25$ Gyrs ago inside its own event horizon $r_{S}=2GM$. The resulting BH had a very low density, $\rho$, and therefore no pressure support, so the collapse continues free fall inside $r_S$, increasing $\rho$ as $\Delta \tau$ square. After $\Delta \tau \simeq 11$ Gyrs, $\rho$ reaches neutron star density and explodes, like a Supernova, into the hot Big Bang expansion that we observe today. The BHU expansion is trapped inside $r_{S}=2GM$, which acts like a cosmological constant $\Lambda=3/r_{S}^2$. The BHU solution follows $R \simeq [r_H^2 r_S]^{1/3}$ so a large fraction of $M$ is outside its Hubble radius $r_H=H^{-1}$. This solves the horizon problem and could be the source for the observed large scale structure (LSS). Thus, the observed cosmic acceleration and LSS could just be caused by the original collapsing $M$, without the need for any exotic Dark Energy or Cosmic Inflation. The observable universe today is larger than $r_{S}$, so we can test this BHU model using Cosmic maps.
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