The universe as a black hole in isotropic coordinates

Abstract

We show that the radial geodesic motion of a particle inside a black hole in isotropic coordinates (the Einstein-Rosen bridge) is physically different from the radial motion inside a Schwarzschild black hole. A particle enters the interior region of an Einstein-Rosen black hole which is regular and physically equivalent to the asymptotically flat exterior of a white hole, and the particle's proper time extends to infinity. Because the motion across the Einstein-Rosen bridge is unidirectional, and the surface of a black hole is the event horizon for distant observers, an Einstein-Rosen black hole is indistinguishable from a Schwarzschild black hole for such observers. Observers inside an Einstein-Rosen black hole perceive its interior as a closed universe that began when the black hole formed, with an initial radius equal to the Schwarzschild radius of the black hole $r_g$, and with an initial accelerated expansion. Therefore the model of a universe as a black hole in isotropic coordinates explains the origin of cosmic inflation. We show that this kind of inflation corresponds to the effective cosmological constant $\Lambda=3/r_g^2$, which, for the smallest astrophysical black holes, is $~10^{-8}m^{-2}$. If we assume that our Universe is the interior of an Einstein-Rosen black hole, astronomical observations give the time of inflation $~10^{-3}s$ and the size of the Universe at the end of the inflationary epoch $~10^{32}m$.