## Methods and Applications of Analysis

- Methods Appl. Anal.
- Volume 11, Number 1 (2004), 077-132.

### Cosmology, Black Holes and Shock Waves Beyond the Hubble Length

#### 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, 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, 2*M*/*r* > 1, and in this sense the shock
wave solution evolves inside a Black Hole. The entropy condition, which
breaks the time symmetry by selecting the explosion over the implosion,
also implies that the shock wave must weaken until it eventually settles
down to a zero pressure OS interface, bounding a *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* = (*c*^{2}/3)
*p*, the equation of state at the earliest stage of Big Bang
physics, is *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 White Hole explosion occurring inside a matter filled universe
that eventually evolves outward through the White Hole event horizon
of an asymptotically flat Schwarzschild spacetime.

#### Article information

**Source**

Methods Appl. Anal., Volume 11, Number 1 (2004), 077-132.

**Dates**

First available in Project Euclid: 15 June 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.maa/1118850852

**Mathematical Reviews number (MathSciNet)**

MR2128353

**Zentralblatt MATH identifier**

1088.83025

#### Citation

Smoller, Joel; Temple, Blake. Cosmology, Black Holes and Shock Waves Beyond the Hubble Length. Methods Appl. Anal. 11 (2004), no. 1, 077--132. https://projecteuclid.org/euclid.maa/1118850852