92 research outputs found
The appearance of coordinate shocks in hyperbolic formalisms of General Realtivity
I consider the appearance of shocks in hyperbolic formalisms of General
Relativity. I study the particular case of the Bona-Masso formalism with zero
shift vector and show how shocks associated with two families of characteristic
fields can develop. These shocks do not represent discontinuities in the
geometry of spacetime, but rather regions where the coordinate system becomes
pathological. For this reason I call them coordinate shocks. I show how one
family of shocks can be eliminated by restricting the Bona-Masso slicing
condition to a special case. The other family of shocks, however, can not be
eliminated even in the case of harmonic slicing. I also show the results of
numerical simulations in the special cases of a flat two-dimensional spacetime,
a flat four-dimensional spacetime with a spherically symmetric slicing, and a
spherically symmetric black hole spacetime. In all three cases coordinate
shocks readily develop, confirming the predictions of the mathematical
analysis. Although here I concentrate in the Bona-Masso formalism, the
phenomena of coordinate shocks should arise in any other hyperbolic formalism.
In particular, since the appearance of the shocks is determined by the choice
of gauge, the results presented here imply that in any formalism the use of a
harmonic slicing can generate shocks.Comment: REVTEX, 27 pages plus 11 Postscript figures. To be published in Phys.
Rev.
The status of numerical relativity
Numerical relativity has come a long way in the last three decades and is now
reaching a state of maturity. We are gaining a deeper understanding of the
fundamental theoretical issues related to the field, from the well posedness of
the Cauchy problem, to better gauge conditions, improved boundary treatment,
and more realistic initial data. There has also been important work both in
numerical methods and software engineering. All these developments have come
together to allow the construction of several advanced fully three-dimensional
codes capable of dealing with both matter and black holes. In this manuscript I
make a brief review the current status of the field.Comment: Report on plenary talk at the 17th International Conference on
General Relativity and Gravitation (GR17), held at Dublin, Ireland, july
2004. Latex, 20 pages, 5 figure
Testing the Cactus code on exact solutions of the Einstein field equations
The article presents a series of numerical simulations of exact solutions of
the Einstein equations performed using the Cactus code, a complete
3-dimensional machinery for numerical relativity. We describe an application
(``thorn'') for the Cactus code that can be used for evolving a variety of
exact solutions, with and without matter, including solutions used in modern
cosmology for modeling the early stages of the universe. Our main purpose has
been to test the Cactus code on these well-known examples, focusing mainly on
the stability and convergence of the code.Comment: 18 pages, 18 figures, Late
Pathologies of hyperbolic gauges in general relativity and other field theories
We present a mathematical characterization of hyperbolic gauge pathologies in
general relativity and electrodynamics. We show how non-linear gauge terms can
produce a blow-up along characteristics and how this can be identified
numerically by performing convergence analysis. Finally, we show some numerical
examples and discuss the profound implications this may have for the field of
numerical relativity.Comment: 5 pages, includes 2 figs. To appear in Phys.Rev.D Rapid Com
Time-Symmetric ADI and Causal Reconnection: Stable Numerical Techniques for Hyperbolic Systems on Moving Grids
Moving grids are of interest in the numerical solution of hydrodynamical
problems and in numerical relativity. We show that conventional integration
methods for the simple wave equation in one and more than one dimension exhibit
a number of instabilities on moving grids. We introduce two techniques, which
we call causal reconnection and time-symmetric ADI, which together allow
integration of the wave equation with absolute local stability in any number of
dimensions on grids that may move very much faster than the wave speed and that
can even accelerate. These methods allow very long time-steps, are fully
second-order accurate, and offer the computational efficiency of
operator-splitting.Comment: 45 pages, 19 figures. Published in 1994 but not previously available
in the electronic archive
Formulations of the 3+1 evolution equations in curvilinear coordinates
Following Brown, in this paper we give an overview of how to modify standard
hyperbolic formulations of the 3+1 evolution equations of General Relativity in
such a way that all auxiliary quantities are true tensors, thus allowing for
these formulations to be used with curvilinear sets of coordinates such as
spherical or cylindrical coordinates. After considering the general case for
both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura
(BSSN) formulations, we specialize to the case of spherical symmetry and also
discuss the issue of regularity at the origin. Finally, we show some numerical
examples of the modified BSSN formulation at work in spherical symmetry.Comment: 19 pages, 12 figure
Astronomy and space on the big screen : how accurately has cinema portrayed space travel and other astrophysical concepts?
Since its origins, cinema has been fascinated with the subject of scientific developments. In particular, astronomy and astrophysics have played an important role in science fiction stories about space travel and exploration. Though the science has not always been accurately represented, in the last decades there has been more and more interest from the cinema industry in approaching scientists to make sure that the stories and concepts shown in films are closer to our true understanding of the universe. In this article, I will explore how cinema has portrayed astrophysical concepts throughout the decades, and how sometimes cinema has even inspired the direction of scientific research
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