4,954 research outputs found
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
Is "the theory of everything'' merely the ultimate ensemble theory?
We discuss some physical consequences of what might be called ``the ultimate
ensemble theory'', where not only worlds corresponding to say different sets of
initial data or different physical constants are considered equally real, but
also worlds ruled by altogether different equations. The only postulate in this
theory is that all structures that exist mathematically exist also physically,
by which we mean that in those complex enough to contain self-aware
substructures (SASs), these SASs will subjectively perceive themselves as
existing in a physically ``real'' world. We find that it is far from clear that
this simple theory, which has no free parameters whatsoever, is observationally
ruled out. The predictions of the theory take the form of probability
distributions for the outcome of experiments, which makes it testable. In
addition, it may be possible to rule it out by comparing its a priori
predictions for the observable attributes of nature (the particle masses, the
dimensionality of spacetime, etc) with what is observed.Comment: 29 pages, revised to match version published in Annals of Physics.
The New Scientist article and color figures are available at
http://www.sns.ias.edu/~max/toe_frames.html or from [email protected]
Matrix General Relativity: A New Look at Old Problems
We develop a novel approach to gravity that we call `matrix general
relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum
version). Gravity is described in this approach not by one Riemannian metric
(i.e. a symmetric two-tensor field) but by a multiplet of such fields, or by a
matrix-valued symmetric two-tensor field that satisfies certain conditions. We
define the matrix extensions of standard constructions of differential geometry
including connections and curvatures, and finally, an invariant functional of
the new field that reduces to the standard Einstein action functional in the
commutative (diagonal) case. Our main idea is the analogy with Yang-Mills
theory (QCD and Standard Model). We call the new degrees of freedom of gravity
associated with the matrix structure `gravitational color' or simply
`gravicolor' and introduce a new gauge symmetry associated with this degree of
freedom. As in the Standard Model there are two possibilities. First of all, it
is possible that at high energies (say at Planckian scale) this symmetry is
exact (symmetric phase), but at low energies it is badly broken, so that one
tensor field remains massless (and gives general relativity) and the other ones
become massive with the masses of Planckian scale. Second possibilty is that
the additional degrees of freedom of gravitational field are confined within
the Planckian scale. What one sees at large distances are singlets (invariants)
of the new gauge symmetry.Comment: 25 page
Time-dependent backgrounds of 2D string theory
We study possible backgrounds of 2D string theory using its equivalence with
a system of fermions in upside-down harmonic potential. Each background
corresponds to a certain profile of the Fermi sea, which can be considered as a
deformation of the hyperbolic profile characterizing the linear dilaton
background. Such a perturbation is generated by a set of commuting flows, which
form a Toda Lattice integrable structure. The flows are associated with all
possible left and right moving tachyon states, which in the compactified theory
have discrete spectrum. The simplest nontrivial background describes the
Sine-Liouville string theory. Our methods can be also applied to the study of
2D droplets of electrons in a strong magnetic field.Comment: 28 pages, 2 figures, lanlma
Post-Minkowskian Gravity: Dark Matter as a Relativistic Inertial Effect?
A review is given of the theory of non-inertial frames (with the associated
inertial effects and the study of the non-relativistic limit) in Minkowski
space-time, of parametrized Minkowski theories and of the rest-frame instant
form of dynamics for isolated systems admitting a Lagrangian description. The
relevance and gauge equivalence of the clock synchronization conventions for
the identification of the instantaneous 3-spaces (Euclidean only in inertial
frames) are described. Then this formalism is applied to tetrad gravity in
globally hyperbolic, asymptotically Minkowskian space-times without
super-translations, where the equivalence principle implies the absence of
global inertial frames. The recently discovered York canonical basis,
diagonalizing the York-Lichnerowicz approach, allows to identify the gauge
variables (inertial effects in general relativity) and the tidal ones (the
gravitational waves of the linearized theory) and to clarify the meaning of the
Hamilton equations. The role of the gauge variable , the trace of the
extrinsic curvature of the non-Euclidean 3-space (the York time not existing in
Newton theory), as a source of inertial effects is emphasized. After the
presentation of preliminary results on the linearization of tetrad gravity in
the family of non-harmonic 3-orthogonal gauges with a free value of , we
define post-Minkowskian gravitational waves (without post-Newtonian
approximations on the matter sources) propagating in a non-Euclidean 3-space,
emphasizing the non-graviton-like aspects of gravity. It is conjectured that
dark matter may be explained as a relativistic inertial effect induced by
: it would simulate the need to choose a privileged gauge connected with
the observational conventions for the description of matter.Comment: 15 pages. Talk at the {\it 1st Mediterranean Conference in Classical
and Quantum Gravity}, held in the Orthodox Academy of Crete in Kolymbari
(Greece) from Monday, September 14th to Friday, September 18th, 200
Network Cosmology
Prediction and control of the dynamics of complex networks is a central
problem in network science. Structural and dynamical similarities of different
real networks suggest that some universal laws might accurately describe the
dynamics of these networks, albeit the nature and common origin of such laws
remain elusive. Here we show that the causal network representing the
large-scale structure of spacetime in our accelerating universe is a power-law
graph with strong clustering, similar to many complex networks such as the
Internet, social, or biological networks. We prove that this structural
similarity is a consequence of the asymptotic equivalence between the
large-scale growth dynamics of complex networks and causal networks. This
equivalence suggests that unexpectedly similar laws govern the dynamics of
complex networks and spacetime in the universe, with implications to network
science and cosmology
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