193 research outputs found
Quantum Einstein-Maxwell Fields: A Unified Viewpoint from the Loop Representation
We propose a naive unification of Electromagnetism and General Relativity
based on enlarging the gauge group of Ashtekar's new variables. We construct
the connection and loop representations and analyze the space of states. In the
loop representation, the wavefunctions depend on two loops, each of them
carrying information about both gravitation and electromagnetism. We find that
the Chern-Simons form and the Jones Polynomial play a role in the model.Comment: 13pp. no figures, Revtex, UU-HEP-92/9, IFFI 92-1
Binary Black Hole Mergers in 3d Numerical Relativity
The standard approach to the numerical evolution of black hole data using the
ADM formulation with maximal slicing and vanishing shift is extended to
non-symmetric black hole data containing black holes with linear momentum and
spin by using a time-independent conformal rescaling based on the puncture
representation of the black holes. We give an example for a concrete three
dimensional numerical implementation. The main result of the simulations is
that this approach allows for the first time to evolve through a brief period
of the merger phase of the black hole inspiral.Comment: 8 pages, 9 figures, REVTeX; expanded discussion, results unchange
Extended Loops: A New Arena for Nonperturbative Quantum Gravity
We propose a new representation for gauge theories and quantum gravity. It
can be viewed as a generalization of the loop representation. We make use of a
recently introduced extension of the group of loops into a Lie Group. This
extension allows the use of functional methods to solve the constraint
equations. It puts in a precise framework the regularization problems of the
loop representation. It has practical advantages in the search for quantum
states. We present new solutions to the Wheeler-DeWitt equation that reinforce
the conjecture that the Jones Polynomial is a state of nonperturbative quantum
gravity.Comment: 12pp, Revtex, no figures, CGPG-93/12-
Ptychographic reconstruction of attosecond pulses
We demonstrate a new attosecond pulse reconstruction modality which uses an
algorithm that is derived from ptychography. In contrast to other methods,
energy and delay sampling are not correlated, and as a result, the number of
electron spectra to record is considerably smaller. Together with the robust
algorithm, this leads to a more precise and fast convergence of the
reconstruction.Comment: 12 pages, 7 figures, the MATLAB code for the method described in this
paper is freely available at
http://figshare.com/articles/attosecond_Extended_Ptychographyc_Iterative_Engine_ePIE_/160187
Multigrid elliptic equation solver with adaptive mesh refinement
In this paper we describe in detail the computational algorithm used by our
parallel multigrid elliptic equation solver with adaptive mesh refinement. Our
code uses truncation error estimates to adaptively refine the grid as part of
the solution process. The presentation includes a discussion of the orders of
accuracy that we use for prolongation and restriction operators to ensure
second order accurate results and to minimize computational work. Code tests
are presented that confirm the overall second order accuracy and demonstrate
the savings in computational resources provided by adaptive mesh refinement.Comment: 12 pages, 9 figures, Modified in response to reviewer suggestions,
added figure, added references. Accepted for publication in J. Comp. Phy
Loop Representations
The loop representation plays an important role in canonical quantum gravity
because loop variables allow a natural treatment of the constraints. In these
lectures we give an elementary introduction to (i) the relevant history of
loops in knot theory and gauge theory, (ii) the loop representation of Maxwell
theory, and (iii) the loop representation of canonical quantum gravity. (Based
on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9
Black-hole binary simulations: the mass ratio 10:1
We present the first numerical simulations of an initially non-spinning
black-hole binary with mass ratio as large as 10:1 in full general relativity.
The binary completes approximately 3 orbits prior to merger and radiates about
0.415% of the total energy and 12.48% of the initial angular momentum in the
form of gravitational waves. The single black hole resulting from the merger
acquires a kick of about 66.7 km/s relative to the original center of mass
frame. The resulting gravitational waveforms are used to validate existing
formulas for the recoil, final spin and radiated energy over a wider range of
the symmetric mass ratio parameter eta=M1*M2/(M1+M2)^2 than previously
possible. The contributions of l > 2 multipoles are found to visibly influence
the gravitational wave signal obtained at fixed inclination angles.Comment: To match published versio
Binary black hole initial data from matched asymptotic expansions
We present an approximate metric for a binary black hole spacetime to
construct initial data for numerical relativity. This metric is obtained by
asymptotically matching a post-Newtonian metric for a binary system to a
perturbed Schwarzschild metric for each hole. In the inner zone near each hole,
the metric is given by the Schwarzschild solution plus a quadrupolar
perturbation corresponding to an external tidal gravitational field. In the
near zone, well outside each black hole but less than a reduced wavelength from
the center of mass of the binary, the metric is given by a post-Newtonian
expansion including the lowest-order deviations from flat spacetime. When the
near zone overlaps each inner zone in a buffer zone, the post-Newtonian and
perturbed Schwarzschild metrics can be asymptotically matched to each other. By
demanding matching (over a 4-volume in the buffer zone) rather than patching
(choosing a particular 2-surface in the buffer zone), we guarantee that the
errors are small in all zones. The resulting piecewise metric is made formally
with smooth transition functions so as to obtain the finite
extrinsic curvature of a 3-slice. In addition to the metric and extrinsic
curvature, we present explicit results for the lapse and the shift, which can
be used as initial data for numerical simulations. This initial data is not
accurate all the way to the asymptotically flat ends inside each hole, and
therefore must be used with evolution codes which employ black hole excision
rather than puncture methods. This paper lays the foundations of a method that
can be sraightforwardly iterated to obtain initial data to higher perturbative
order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing
of text, no major change to the physic
Radiation from low-momentum zoom-whirl orbits
We study zoom-whirl behaviour of equal mass, non-spinning black hole binaries
in full general relativity. The magnitude of the linear momentum of the initial
data is fixed to that of a quasi-circular orbit, and its direction is varied.
We find a global maximum in radiated energy for a configuration which completes
roughly one orbit. The radiated energy in this case exceeds the value of a
quasi-circular binary with the same momentum by 15%. The direction parameter
only requires minor tuning for the localization of the maximum. There is
non-trivial dependence of the energy radiated on eccentricity (several local
maxima and minima). Correlations with orbital dynamics shortly before merger
are discussed. While being strongly gauge dependent, these findings are
intuitive from a physical point of view and support basic ideas about the
efficiency of gravitational radiation from a binary system.Comment: 9 pages, 6 figures, Amaldi8 conference proceedings as publishe
Numerical evolution of multiple black holes with accurate initial data
We present numerical evolutions of three equal-mass black holes using the
moving puncture approach. We calculate puncture initial data for three black
holes solving the constraint equations by means of a high-order multigrid
elliptic solver. Using these initial data, we show the results for three black
hole evolutions with sixth-order waveform convergence. We compare results
obtained with the BAM and AMSS-NCKU codes with previous results. The
approximate analytic solution to the Hamiltonian constraint used in previous
simulations of three black holes leads to different dynamics and waveforms. We
present some numerical experiments showing the evolution of four black holes
and the resulting gravitational waveform.Comment: Published in PR
- …