22 research outputs found
How much energy do closed timelike curves in 2+1 spacetimes need?
By noticing that, in open 2+1 gravity, polarized surfaces cannot converge in
the presence of timelike total energy momentum (except for a rotation of 2 pi),
we give a simple argument which shows that, quite generally, closed timelike
curves cannot exist in the presence of such energy condition.Comment: 3 pages, with no figures. Accepted in PRD as Rapid Communicatio
3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints
We present three-dimensional simulations of Einstein equations implementing a
symmetric hyperbolic system of equations with dynamical lapse. The numerical
implementation makes use of techniques that guarantee linear numerical
stability for the associated initial-boundary value problem. The code is first
tested with a gauge wave solution, where rather larger amplitudes and for
significantly longer times are obtained with respect to other state of the art
implementations. Additionally, by minimizing a suitably defined energy for the
constraints in terms of free constraint-functions in the formulation one can
dynamically single out preferred values of these functions for the problem at
hand. We apply the technique to fully three-dimensional simulations of a
stationary black hole spacetime with excision of the singularity, considerably
extending the lifetime of the simulations.Comment: 21 pages. To appear in PR
Exotic spacetimes, superconducting strings with linear momentum, and (not quite) all that
We derive the general exact vacuum metrics associated with a stationary (non
static), non rotating, cylindrically symmetric source. An analysis of the
geometry described by these vacuum metrics shows that they contain a subfamily
of metrics that, although admitting a consistent time orientation, display
"exotic" properties, such as "trapping" of geodesics and closed causal curves
through every point. The possibility that such spacetimes could be generated by
a superconducting string, endowed with a neutral current and momentum, has
recently been considered by Thatcher and Morgan. Our results, however, differ
from those found by Thatcher and Morgan, and the discrepancy is explained. We
also analyze the general possibility of constructing physical sources for the
exotic metrics, and find that, under certain restrictions, they must always
violate the dominant energy condition (DEC). We illustrate our results by
explicitly analyzing the case of concentric shells, where we find that in all
cases the external vacuum metric is non exotic if the matter in the shells
satisfies the DEC.Comment: 13 pages with no figures. Accepted in PR
Numerical simulations with a first order BSSN formulation of Einstein's field equations
We present a new fully first order strongly hyperbolic representation of the
BSSN formulation of Einstein's equations with optional constraint damping
terms. We describe the characteristic fields of the system, discuss its
hyperbolicity properties, and present two numerical implementations and
simulations: one using finite differences, adaptive mesh refinement and in
particular binary black holes, and another one using the discontinuous Galerkin
method in spherical symmetry. The results of this paper constitute a first step
in an effort to combine the robustness of BSSN evolutions with very high
accuracy numerical techniques, such as spectral collocation multi-domain or
discontinuous Galerkin methods.Comment: To appear in Physical Review
The discrete energy method in numerical relativity: Towards long-term stability
The energy method can be used to identify well-posed initial boundary value
problems for quasi-linear, symmetric hyperbolic partial differential equations
with maximally dissipative boundary conditions. A similar analysis of the
discrete system can be used to construct stable finite difference equations for
these problems at the linear level. In this paper we apply these techniques to
some test problems commonly used in numerical relativity and observe that while
we obtain convergent schemes, fast growing modes, or ``artificial
instabilities,'' contaminate the solution. We find that these growing modes can
partially arise from the lack of a Leibnitz rule for discrete derivatives and
discuss ways to limit this spurious growth.Comment: 18 pages, 22 figure
Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations
We present new many-parameter families of strongly and symmetric hyperbolic
formulations of Einstein's equations that include quite general algebraic and
live gauge conditions for the lapse. The first system that we present has 30
variables and incorporates an algebraic relationship between the lapse and the
determinant of the three metric that generalizes the densitized lapse
prescription. The second system has 34 variables and uses a family of live
gauges that generalizes the Bona-Masso slicing conditions. These systems have
free parameters even after imposing hyperbolicity and are expected to be useful
in 3D numerical evolutions. We discuss under what conditions there are no
superluminal characteristic speeds
Large quantum gravity effects and nonlocal variables
We reconsider here the model where large quantum gravity effects were first
found, but now in its Null Surface Formulation (NSF). We find that although the
set of coherent states for , the basic variable of NSF, is as restricted as
it is the one for the metric, while some type of small deviations from these
states may cause huge fluctuations on the metric, the corresponding
fluctuations on remain small.Comment: 4 pages, accepted in PR
No Time Machine Construction in Open 2+1 Gravity with Timelike Total Energy Momentum
It is shown that in 2+1 dimensional gravity an open spacetime with timelike
sources and total energy momentum cannot have a stable compactly generated
Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and
shows, in particular, that not only a Gott pair cannot be formed from processes
such as the decay of a single cosmic string as has been shown by Carroll et
al., but that, in a precise sense, a time machine cannot be constructed at all.Comment: 7 pages. Several changes and 3 figures added. To appear in Phys. Rev.