1,112 research outputs found
Head-on collisions of boson stars
We study head-on collisions of boson stars in three dimensions. We consider
evolutions of two boson stars which may differ in their phase or have opposite
frequencies but are otherwise identical. Our studies show that these phase
differences result in different late time behavior and gravitational wave
output
Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
We study the stability of three-dimensional numerical evolutions of the
Einstein equations, comparing the standard ADM formulation to variations on a
family of formulations that separate out the conformal and traceless parts of
the system. We develop an implementation of the conformal-traceless (CT)
approach that has improved stability properties in evolving weak and strong
gravitational fields, and for both vacuum and spacetimes with active coupling
to matter sources. Cases studied include weak and strong gravitational wave
packets, black holes, boson stars and neutron stars. We show under what
conditions the CT approach gives better results in 3D numerical evolutions
compared to the ADM formulation. In particular, we show that our implementation
of the CT approach gives more long term stable evolutions than ADM in all the
cases studied, but is less accurate in the short term for the range of
resolutions used in our 3D simulations.Comment: 17 pages, 15 figures. Small changes in the text, and a change in the
list of authors. One new reference adde
Phantom Field from Conformal Invariance
We establish a correspondence between a conformally invariant complex scalar
field action (with a conformal self-interaction potential) and the action of a
phantom scalar field minimally coupled to gravity (with a cosmological
constant). In this correspondence, the module of the complex scalar field is
used to relate conformally the metrics of both systems while its phase is
identified with the phantom scalar field. At the level of the equations, the
correspondence allows to map solution of the conformally non-linear
Klein-Gordon equation with vanishing energy-momentum tensor to solution of a
phantom scalar field minimally coupled to gravity with cosmological constant
satisfying a massless Klein-Gordon equation. The converse is also valid with
the advantage that it offers more possibilities owing to the freedom of
rewriting a metric as the conformal transformation of another metric. Finally,
we provide some examples of this correspondence.Comment: 5 pages, two column
The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
A modern re-visitation of the consequences of the lack of an intrinsic notion
of instantaneous 3-space in relativistic theories leads to a reformulation of
their kinematical basis emphasizing the role of non-inertial frames centered on
an arbitrary accelerated observer. In special relativity the exigence of
predictability implies the adoption of the 3+1 point of view, which leads to a
well posed initial value problem for field equations in a framework where the
change of the convention of synchronization of distant clocks is realized by
means of a gauge transformation. This point of view is also at the heart of the
canonical approach to metric and tetrad gravity in globally hyperbolic
asymptotically flat space-times, where the use of Shanmugadhasan canonical
transformations allows the separation of the physical degrees of freedom of the
gravitational field (the tidal effects) from the arbitrary gauge variables.
Since a global vision of the equivalence principle implies that only global
non-inertial frames can exist in general relativity, the gauge variables are
naturally interpreted as generalized relativistic inertial effects, which have
to be fixed to get a deterministic evolution in a given non-inertial frame. As
a consequence, in each Einstein's space-time in this class the whole
chrono-geometrical structure, including also the clock synchronization
convention, is dynamically determined and a new approach to the Hole Argument
leads to the conclusion that "gravitational field" and "space-time" are two
faces of the same entity. This view allows to get a classical scenario for the
unification of the four interactions in a scheme suited to the description of
the solar system or our galaxy with a deperametrization to special relativity
and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of
Theoretical Physics, "Current Mathematical Topics in Gravitation and
Cosmology", Ladek, Poland, 6-11 February 200
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Numerical Relativity: A review
Computer simulations are enabling researchers to investigate systems which
are extremely difficult to handle analytically. In the particular case of
General Relativity, numerical models have proved extremely valuable for
investigations of strong field scenarios and been crucial to reveal unexpected
phenomena. Considerable efforts are being spent to simulate astrophysically
relevant simulations, understand different aspects of the theory and even
provide insights in the search for a quantum theory of gravity. In the present
article I review the present status of the field of Numerical Relativity,
describe the techniques most commonly used and discuss open problems and (some)
future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and
Quantum Gravity. (uses iopart.cls
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