737 research outputs found
Why Solve the Hamiltonian Constraint in Numerical Relativity?
The indefinite sign of the Hamiltonian constraint means that solutions to
Einstein's equations must achieve a delicate balance--often among numerically
large terms that nearly cancel. If numerical errors cause a violation of the
Hamiltonian constraint, the failure of the delicate balance could lead to
qualitatively wrong behavior rather than just decreased accuracy. This issue is
different from instabilities caused by constraint-violating modes. Examples of
stable numerical simulations of collapsing cosmological spacetimes exhibiting
local mixmaster dynamics with and without Hamiltonian constraint enforcement
are presented.Comment: Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk
given at GR1
High velocity spikes in Gowdy spacetimes
We study the behavior of spiky features in Gowdy spacetimes. Spikes with
velocity initially high are, generally, driven to low velocity. Let n be any
integer greater than or equal to 1. If the initial velocity of an upward
pointing spike is between 4n-3 and 4n-1 the spike persists with final velocity
between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the
spiky feature eventually disappears. For downward pointing spikes the analogous
rule is that spikes with initial velocity between 4n-4 and 4n-2 persist with
final velocity between 0 and 1, while spikes with initial velocity between 4n-2
and 4n eventually disappear.Comment: discussion of constraints added. Accepted for publication in Phys.
Rev.
On Singularity Resolution in Quantum Gravity
We examine the singularity resolution issue in quantum gravity by studying a
new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The
quantization procedure is inspired by the loop quantum gravity programme, and
is based on an alternative to the Schr\"odinger representation normally used in
metric variable quantum cosmology. We show that in this representation for
quantum geometrodynamics there exists a densely defined inverse scale factor
operator, and that the Hamiltonian constraint acts as a difference operator on
the basis states. We find that the cosmological singularity is avoided in the
quantum dynamics. We discuss these results with a view to identifying the
criteria that constitute "singularity resolution" in quantum gravity.Comment: 12 page
Phenomenology of the Gowdy Universe on
Numerical studies of the plane symmetric, vacuum Gowdy universe on yield strong support for the conjectured asymptotically velocity term
dominated (AVTD) behavior of its evolution toward the singularity except,
perhaps, at isolated spatial points. A generic solution is characterized by
spiky features and apparent ``discontinuities'' in the wave amplitudes. It is
shown that the nonlinear terms in the wave equations drive the system
generically to the ``small velocity'' AVTD regime and that the spiky features
are caused by the absence of these terms at isolated spatial points.Comment: 19 pages, 21 figures, uses Revtex, psfi
Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes
We set up the singular initial value problem for quasilinear hyperbolic
Fuchsian systems of first order and establish an existence and uniqueness
theory for this problem with smooth data and smooth coefficients (and with even
lower regularity). We apply this theory in order to show the existence of
smooth (generally not analytic) T2-symmetric solutions to the vacuum Einstein
equations, which exhibit AVTD (asymptotically velocity term dominated) behavior
in the neighborhood of their singularities and are polarized or half-polarized.Comment: 78 page
Semiclassical evaluation of average nuclear one and two body matrix elements
Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged
on the energy shell, on the basis of independent particle Hamiltonians. One-
and two-body matrix elements are compared with the quantal results and it is
demonstrated that the semiclassical matrix elements, as function of energy,
well pass through the average of the scattered quantum values. For the one-body
matrix elements it is shown how the Thomas-Fermi approach can be projected on
good parity and also on good angular momentum. For the two-body case the
pairing matrix elements are considered explicitly.Comment: 15 pages, REVTeX, 6 ps figures; changed conten
Analytic approximation and an improved method for computing the stress-energy of quantized scalar fields in Robertson-Walker spacetimes
An improved method is given for the computation of the stress-energy tensor
of a quantized scalar field using adiabatic regularization. The method works
for fields with arbitrary mass and curvature coupling in Robertson-Walker
spacetimes and is particularly useful for spacetimes with compact spatial
sections. For massless fields it yields an analytic approximation for the
stress-energy tensor that is similar in nature to those obtained previously for
massless fields in static spacetimes.Comment: RevTeX, 8 pages, no figure
A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
We investigate the initial value problem for the Einstein-Euler equations of
general relativity under the assumption of Gowdy symmetry on T3, and we
construct matter spacetimes with low regularity. These spacetimes admit, both,
impulsive gravitational waves in the metric (for instance, Dirac mass curvature
singularities propagating at light speed) and shock waves in the fluid (i.e.,
discontinuities propagating at about the sound speed). Given an initial data
set, we establish the existence of a future development and we provide a global
foliation in terms of a globally and geometrically defined time-function,
closely related to the area of the orbits of the symmetry group. The main
difficulty lies in the low regularity assumed on the initial data set which
requires a distributional formulation of the Einstein-Euler equations.Comment: 24 page
Dynamics of Brane-World Cosmological Models
We show that generically the initial singularity is isotropic in spatially
homogeneous cosmological models in the brane-world scenario. We then argue that
it is plausible that the initial singularity is isotropic in typical brane
world cosmological models. Therefore, brane cosmology naturally gives rise to a
set of initial data that provide the conditions for inflation to subsequently
take place, thereby solving the initial conditions problem and leading to a
self--consistent and viable cosmology.Comment: Final version. To appear in Physical Revie
No-horizon theorem for vacuum gravity with spacelike G1 isometry groups
We show that (3+1) vacuum spacetimes admitting a global, spacelike,
one-parameter Lie group of isometries of translational type cannot contain
apparent horizons. The only assumption made is that of the existence of a
global spacelike Killing vector field with infinite open orbits; the
four-dimensional vacuum spacetime metric is otherwise arbitrary. This result
may thus be viewed as a hoop conjecture theorem for vacuum gravity with one
spacelike translational Killing symmetry.Comment: 6 pages, revtex4; published in Phys. Rev. D Rapid Com
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