487 research outputs found
Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
General relativity is a deterministic theory with non-fixed causal structure.
Quantum theory is a probabilistic theory with fixed causal structure. In this
paper we build a framework for probabilistic theories with non-fixed causal
structure. This combines the radical elements of general relativity and quantum
theory. The key idea in the construction is physical compression. A physical
theory relates quantities. Thus, if we specify a sufficiently large set of
quantities (this is the compressed set), we can calculate all the others. We
apply three levels of physical compression. First, we apply it locally to
quantities (actually probabilities) that might be measured in a particular
region of spacetime. Then we consider composite regions. We find that there is
a second level of physical compression for the composite region over and above
the first level physical compression for the component regions. Each
application of first and second level physical compression is quantified by a
matrix. We find that these matrices themselves are related by the physical
theory and can therefore be subject to compression. This is the third level of
physical compression. This third level of physical compression gives rise to a
new mathematical object which we call the causaloid. From the causaloid for a
particular physical theory we can calculate verything the physical theory can
calculate. This approach allows us to set up a framework for calculating
probabilistic correlations in data without imposing a fixed causal structure
(such as a background time). We show how to put quantum theory in this
framework (thus providing a new formulation of this theory). We indicate how
general relativity might be put into this framework and how the framework might
be used to construct a theory of quantum gravity.Comment: 23 pages. For special issue of Journal of Physics A entitled "The
quantum universe" in honour of Giancarlo Ghirard
Second order perturbations of a Schwarzschild black hole: inclusion of odd parity perturbations
We consider perturbations of a Schwarzschild black hole that can be of both
even and odd parity, keeping terms up to second order in perturbation theory,
for the axisymmetric case. We develop explicit formulae for the
evolution equations and radiated energies and waveforms using the
Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for
the treatment in the ``close limit approximation'' of the collision of
counterrotating black holes.Comment: 12 pages RevTe
Criticality in the collapse of spherically symmetric massless scalar fields in semi-classical loop quantum gravity
In a recent paper we showed that the collapse to a black hole in
one-parameter families of initial data for massless, minimally coupled scalar
fields in spherically symmetric semi-classical loop quantum gravity exhibited a
universal mass scaling similar to the one in classical general relativity. In
particular, no evidence of a mass gap appeared as had been suggested by
previous studies. The lack of a mass gap indicated the possible existence of a
self-similar critical solution as in general relativity. Here we provide
further evidence for its existence. Using an adaptive mesh refinement code, we
show that "echoes" arise as a result of the discrete self-similarity in
space-time. We also show the existence of "wiggles" in the mass scaling
relation, as in the classical theory. The results from the semi-classical
theory agree well with those of classical general relativity unless one takes
unrealistically large values for the polymerization parameter.Comment: 7 pages, RevTe
The Lazarus Project. II. Spacelike extraction with the quasi-Kinnersley tetrad
The Lazarus project was designed to make the most of limited 3D binary
black-hole simulations, through the identification of perturbations at late
times, and subsequent evolution of the Weyl scalar via the Teukolsky
formulation. Here we report on new developments, employing the concept of the
``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to
analyze late-time numerical spacetimes that should differ only slightly from
Kerr. This allows us to extract the essential information about the background
Kerr solution, and through this, to identify the radiation present. We
explicitly test this procedure with full numerical evolutions of Bowen-York
data for single spinning black holes, head-on and orbiting black holes near the
ISCO regime. These techniques can be compared with previous Lazarus results,
providing a measure of the numerical-tetrad errors intrinsic to the method, and
give as a by-product a more robust wave extraction method for numerical
relativity.Comment: 17 pages, 10 figures. Journal version with text changes, revised
figures. [Note updated version of original Lazarus paper (gr-qc/0104063)
Uniform discretizations: a quantization procedure for totally constrained systems including gravity
We present a new method for the quantization of totally constrained systems
including general relativity. The method consists in constructing discretized
theories that have a well defined and controlled continuum limit. The discrete
theories are constraint-free and can be readily quantized. This provides a
framework where one can introduce a relational notion of time and that
nevertheless approximates in a well defined fashion the theory of interest. The
method is equivalent to the group averaging procedure for many systems where
the latter makes sense and provides a generalization otherwise. In the
continuum limit it can be shown to contain, under certain assumptions, the
``master constraint'' of the ``Phoenix project''. It also provides a
correspondence principle with the classical theory that does not require to
consider the semiclassical limit.Comment: 4 pages, Revte
Evolution systems for non-linear perturbations of background geometries
The formulation of the initial value problem for the Einstein equations is at
the heart of obtaining interesting new solutions using numerical relativity and
still very much under theoretical and applied scrutiny. We develop a
specialised background geometry approach, for systems where there is
non-trivial a priori knowledge about the spacetime under study. The background
three-geometry and associated connection are used to express the ADM evolution
equations in terms of physical non-linear deviations from that background.
Expressing the equations in first order form leads naturally to a system
closely linked to the Einstein-Christoffel system, introduced by Anderson and
York, and sharing its hyperbolicity properties. We illustrate the drastic
alteration of the source structure of the equations, and discuss why this is
likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in
Physical Review
Inspiral, merger and ring-down of equal-mass black-hole binaries
We investigate the dynamics and gravitational-wave (GW) emission in the
binary merger of equal-mass black holes as obtained from numerical relativity
simulations. Results from the evolution of three sets of initial data are
explored in detail, corresponding to different initial separations of the black
holes. We find that to a good approximation the inspiral phase of the evolution
is quasi-circular, followed by a "blurred, quasi-circular plunge", then merger
and ring down. We present first-order comparisons between analytical models of
the various stages of the merger and the numerical results. We provide
comparisons between the numerical results and analytical predictions based on
the adiabatic Newtonain, post-Newtonian (PN), and non-adiabatic resummed-PN
models. From the ring-down portion of the GW we extract the fundamental
quasi-normal mode and several of the overtones. Finally, we estimate the
optimal signal-to-noise ratio for typical binaries detectable by GW
experiments.Comment: 47 pages, 34 figures, full abstract in paper, revtex4, accepted by
PRD, miscellaneous revisions throughout pape
Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
We generalize the idea of Vassiliev invariants to the spin network context,
with the aim of using these invariants as a kinematical arena for a canonical
quantization of gravity. This paper presents a detailed construction of these
invariants (both ambient and regular isotopic) requiring a significant
elaboration based on the use of Chern-Simons perturbation theory which extends
the work of Kauffman, Martin and Witten to four-valent networks. We show that
this space of knot invariants has the crucial property -from the point of view
of the quantization of gravity- of being loop differentiable in the sense of
distributions. This allows the definition of diffeomorphism and Hamiltonian
constraints. We show that the invariants are annihilated by the diffeomorphism
constraint. In a companion paper we elaborate on the definition of a
Hamiltonian constraint, discuss the constraint algebra, and show that the
construction leads to a consistent theory of canonical quantum gravity.Comment: 21 Pages, RevTex, many figures included with psfi
Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer-Meshkov instability
The effects of seed magnetic fields on the Richtmyer-Meshkov instability driven by converging cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Two different seed field configurations at various strengths are applied over a cylindrical or spherical density interface which has a single-dominant-mode perturbation. The shocks that excite the instability are generated with appropriate Riemann problems in a numerical formulation and the effect of the seed field on the growth rate and symmetry of the perturbations on the density interface is examined. We find reduced perturbation growth for both field configurations and all tested strengths. The extent of growth suppression increases with seed field strength but varies with the angle of the field to interface. The seed field configuration does not significantly affect extent of suppression of the instability, allowing it to be chosen to minimize its effect on implosion distortion. However, stronger seed fields are required in three dimensions to suppress the instability effectively
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