251 research outputs found
Cosmology, Black Holes and Shock Waves Beyond the Hubble Length
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, 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 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
Cosmology with a shock wave
We construct the simplest solution of the Einstein equations that
incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric
whose equation of state accounts for the Hubble constant and the microwave
background radiation temperature. This produces a new solution of the Einstein
equations from which we are able to derive estimates for the shock position at
present time. We show that the distance from the shock-wave to the center of
the explosion at present time is comparable to the Hubble distance. We are
motivated by the idea that the expansion of the universe as measured by the
Hubble constant might be accounted for by an event more similar to a classical
explosion than by the well-accepted scenario of the Big Bang
"Regularity Singularities" and the Scattering of Gravity Waves in Approximate Locally Inertial Frames
It is an open question whether solutions of the Einstein-Euler equations are
smooth enough to admit locally inertial coordinates at points of shock wave
interaction, or whether "regularity singularities" can exist at such points.
The term {\it regularity singularity} was proposed by the authors as a point in
spacetime where the gravitational metric tensor is Lipschitz continuous
(), but no smoother, in any coordinate system of the atlas.
An existence theory for shock wave solutions in admitting arbitrary
interactions has been proven for the Einstein-Euler equations in spherically
symmetric spacetimes, but is the requisite smoothness required for
space-time to be locally flat. Thus the open problem of regularity
singularities is the problem as to whether locally inertial coordinate systems
exist at shock waves within the larger atlas. To clarify this open
problem, we identify new "Coriolis type" effects in the geometry of
shock wave metrics and prove they are essential in the sense that they can
never be made to vanish within the atlas of {\it smooth} coordinate
transformations, the atlas usually assumed in classical differential geometry.
Thus the problem of existence of regularity singularities is equivalent to the
question as to whether or not these Coriolis type effects are essentially
non-removable and `real', or merely coordinate effects that can be removed, (in
analogy to classical Coriolis forces), by going to the less regular atlas of
transformations. If essentially non-removable, it would argue
strongly for a `real' new physical effect for General Relativity, providing a
physical context to the open problem of regularity singularities.Comment: 29 pages. Version 2: Corrections of some typographical errors and
improvements of wording. Results are unchange
Shock-Wave Cosmology Inside a Black Hole
We construct a class of global exact solutions of the Einstein equations that
extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\em
inside the Black Hole}, by incorporating a shock wave at the leading edge of
the expansion of the galaxies, arbitrarily far beyond the Hubble length in the
Friedmann-Robertson-Walker (FRW) spacetime. Here the expanding FRW universe
emerges behind a subluminous blast wave that explodes outward from the FRW
center at the instant of the Big Bang. The total mass behind the shock
decreases as the shock wave expands, and the entropy condition implies that the
shock wave must weaken to the point where it settles down to an OS interface,
(bounding a {\em finite} total mass), that eventually emerges from the White
Hole event horizon of an ambient Schwarzschild spacetime. The entropy condition
breaks the time symmetry of the Einstein equations, selecting the explosion
over the implosion. 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 a Schwarzschild spacetime.Comment: Small corrections that significantly improve the result
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