Cosmology, Black Holes and Shock Waves Beyond the Hubble Length

TL;DR

This paper develops exact shock wave solutions within Einstein's equations, proposing a novel cosmological model where the Big Bang originates from a localized explosion inside a black hole, with implications for universe expansion and uniformity.

Contribution

It introduces a new class of entropy satisfying shock wave solutions extending the OS model to non-zero pressure inside black holes, forming the basis for a novel cosmological scenario.

Findings

Shock waves lie beyond one Hubble length from the FRW center.

Shock wave eventually weakens and settles to a zero-pressure interface.

The Big Bang shock wave emerges at the speed of light for a specific equation of state.

Abstract

We construct exact, entropy satisfying shock wave solutions of the Einstein equations for a perfect fluid which extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\it inside the Black Hole}. These solutions put forth a new Cosmological Model in which the expanding Friedmann-Robertson-Walker (FRW) universe emerges from the Big Bang with a shock wave at the leading edge of the expansion, analogous to a classical shock wave explosion. This explosion is large enough to account for the enormous scale on which the galaxies and the background radiation appear uniform. In these models, the shock wave must lie beyond one Hubble length from the FRW center, this threshhold being the boundary across which the bounded mass lies inside its own Schwarzshild radius, $2M/r>1,$ and thus the shock wave solution evolves inside a Black Hole. The entropy condition, which breaks the time symmetry, implies that the shock wave must weaken until it eventually settles down to a zero pressure OS interface, bounding a {\em finite} total mass, that emerges from the White Hole event horizon of an ambient Schwarzschild spacetime. However, unlike shock matching outside a Black Hole, the equation of state $p=\frac{c^2}{3}\rho,$ the equation of state at the earliest stage of Big Bang physics, is {\em distinguished} at the instant of the Big Bang--for this equation of state alone, the shock wave emerges from the Big Bang at a finite nonzero speed, the speed of light, decelerating to a subluminous wave from that time onward. These shock wave solutions indicate a new cosmological model in which the Big Bang arises from a localized explosion occurring inside the Black Hole of an asymptotically flat Schwarzschild spacetime.