211 research outputs found
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
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
Decay of Solutions of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry
We prove that the Schwarzschild black hole is linearly stable under
electromagnetic and gravitational perturbations. Our method is to show that for
spin or , solutions of the Teukolsky equation with smooth, compactly
supported initial data outside the event horizon, decay in .Comment: 32 pages, LaTeX, 2 figures, error in expression for energy density of
gravitational waves correcte
Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions
We derive WKB approximations for a class of Airy and parabolic cylinder
functions in the complex plane, including quantitative error bounds. We prove
that all zeros of the Airy function lie on a ray in the complex plane, and that
the parabolic cylinder functions have no zeros. We also analyze the Airy and
Airy-WKB limit of the parabolic cylinder functions.Comment: 25 pages, LaTeX, 7 figures (published version
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
Rotating Fluids with Self-Gravitation in Bounded Domains
In this paper, we study the steady solutions of Euler-Poisson equations in
bounded domains with prescribed angular velocity. This models a rotating
Newtonian star consisting of a compressible perfect fluid with given equation
of state . When the domain is a ball and the angular
velocity is constant, we obtain both existence and non-existence theorems,
depending on the adiabatic gas constant . In addition we obtain some
interesting properties of the solutions; e.g., monotonicity of the radius of
the star with both angular velocity and central density. We also prove that the
radius of a rotating spherically symmetric star, with given constant angular
velocity and constant entropy, is uniformly bounded independent of the central
density . This is physically striking and in sharp contrast to the case of the
nonrotating star. For general domains and variable angular velocities, both an
existence result for the isentropic equations of state and non-existence result
for the non-isentropic equation of state are also obtained.Comment: 37page
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