1,754 research outputs found
Elastic shocks in relativistic rigid rods and balls
We study the free boundary problem for the "hard phase" material introduced
by Christodoulou, both for rods in (1+1)-dimensional Minkowski spacetime and
for spherically symmetric balls in (3+1)-dimensional Minkowski spacetime.
Unlike Christodoulou, we do not consider a "soft phase", and so we regard this
material as an elastic medium, capable of both compression and stretching. We
prove that shocks must be null hypersurfaces, and derive the conditions to be
satisfied at a free boundary. We solve the equations of motion of the rods
explicitly, and we prove existence of solutions to the equations of motion of
the spherically symmetric balls for an arbitrarily long (but finite) time,
given initial conditions sufficiently close to those for the relaxed ball at
rest. In both cases we find that the solutions contain shocks if and only if
the pressure or its time derivative do not vanish at the free boundary
initially. These shocks interact with the free boundary, causing it to lose
regularity.Comment: 22 pages, 3 figures; v2: small changes, matches final published
version; v3: typos in the references fixe
The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant
Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.info:eu-repo/semantics/submittedVersio
The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant
Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.info:eu-repo/semantics/submittedVersio
Spherical linear waves in de Sitter spacetime
We apply Christodoulou's framework, developed to study the Einstein-scalar
field equations in spherical symmetry, to the linear wave equation in de Sitter
spacetime, as a first step towards the Einstein-scalar field equations with
positive cosmological constant. We obtain an integro-differential evolution
equation which we solve by taking initial data on a null cone. As a corollary
we obtain elementary derivations of expected properties of linear waves in de
Sitter spacetime: boundedness in terms of (characteristic) initial data, and a
Price law establishing uniform exponential decay, in Bondi time, to a constant.Comment: 9 pages, 1 figure; v2: minor changes, references added, matches final
published versio
Strong cosmic censorship: The nonlinear story
A satisfactory formulation of the laws of physics entails that the future
evolution of a physical system should be determined from appropriate initial
conditions. The existence of Cauchy horizons in solutions of the Einstein field
equations is therefore problematic, and expected to be an unstable artifact of
General Relativity. This is asserted by the Strong Cosmic Censorship
Conjecture, which was recently put into question by an analysis of the
linearized equations in the exterior of charged black holes in an expanding
universe. Here, we numerically evolve the nonlinear Einstein-Maxwell-scalar
field equations with a positive cosmological constant, under spherical
symmetry, and provide strong evidence that mass inflation indeed does not occur
in the near extremal regime. This shows that nonlinear effects might not
suffice to save the Strong Cosmic Censorship Conjecture.Comment: 9 pages, 8 figures. v2: Matches published versio
On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions
This paper is the third part of a trilogy dedicated to the following problem:
given spherically symmetric characteristic initial data for the
Einstein-Maxwell-scalar field system with a cosmological constant ,
with the data on the outgoing initial null hypersurface given by a subextremal
Reissner-Nordstrom black hole event horizon, study the future extendibility of
the corresponding maximal globally hyperbolic development as a "suitably
regular" Lorentzian manifold.
In the first part of this series we established the well posedness of the
characteristic problem, whereas in the second part we studied the stability of
the radius function at the Cauchy horizon.
In this third and final paper we show that, depending on the decay rate of
the initial data, mass inflation may or may not occur. When the mass is
controlled, it is possible to obtain continuous extensions of the metric across
the Cauchy horizon with square integrable Christoffel symbols. Under slightly
stronger conditions, we can bound the gradient of the scalar field. This allows
the construction of (non-isometric) extensions of the maximal development which
are classical solutions of the Einstein equations. Our results provide evidence
against the validity of the strong cosmic censorship conjecture when
.Comment: 48 pages, 5 figures; v2: some presentation changes, mostly in the
Introduction; v3: substantial changes in Section 5; v4: expanded
Introduction; some presentation changes; matches final published versio
Mass, angular-momentum, and charge inequalities for axisymmetric initial data
We present the key elements of the proof of an upper bound for
angular-momentum and charge in terms of the mass for electro-vacuum
asymptotically flat axisymmetric initial data sets with simply connected orbit
space
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