125 research outputs found
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
Constants of motion for vacuum general relativity
The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting
spacelike Killing vector fields, may be written as the equations of the
principal chiral model with certain `source' terms. Using this
formulation, we give a procedure for generating an infinite number of non-local
constants of motion for this sector of the Einstein equations. The constants of
motion arise as explicit functionals on the phase space of Einstein gravity,
and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
A Connection Approach to Numerical Relativity
We discuss a general formalism for numerically evolving initial data in
general relativity in which the (complex) Ashtekar connection and the
Newman-Penrose scalars are taken as the dynamical variables. In the generic
case three gauge constraints and twelve reality conditions must be solved. The
analysis is applied to a Petrov type \{1111\} planar spacetime where we find a
spatially constant volume element to be an appropriate coordinate gauge choice.Comment: 17 pages, LaTe
Einstein's equations and the chiral model
The vacuum Einstein equations for spacetimes with two commuting spacelike
Killing field symmetries are studied using the Ashtekar variables. The case of
compact spacelike hypersurfaces which are three-tori is considered, and the
determinant of the Killing two-torus metric is chosen as the time gauge. The
Hamiltonian evolution equations in this gauge may be rewritten as those of a
modified SL(2) principal chiral model with a time dependent `coupling
constant', or equivalently, with time dependent SL(2) structure constants. The
evolution equations have a generalized zero-curvature formulation. Using this
form, the explicit time dependence of an infinite number of
spatial-diffeomorphism invariant phase space functionals is extracted, and it
is shown that these are observables in the sense that they Poisson commute with
the reduced Hamiltonian. An infinite set of observables that have SL(2) indices
are also found. This determination of the explicit time dependence of an
infinite set of spatial-diffeomorphism invariant observables amounts to the
solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.
Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
A reducible representation of the Temperley-Lieb algebra is constructed on
the tensor product of n-dimensional spaces. One obtains as a centraliser of
this action a quantum algebra (a quasi-triangular Hopf algebra) U_q with a
representation ring equivalent to the representation ring of the sl_2 Lie
algebra. This algebra U_q is the symmetry algebra of the corresponding open
spin chain.Comment: 14 pages LaTex; typos corrected and two references adde
Direct evidence for shock-powered optical emission in a nova
Classical novae are thermonuclear explosions that occur on the surfaces of white dwarf stars in interacting binary systems1. It has long been thought that the luminosity of classical novae is powered by continued nuclear burning on the surface of the white dwarf after the initial runaway2. However, recent observations of gigaelectronvolt Îł-rays from classical novae have hinted that shocks internal to the nova ejecta may dominate the nova emission. Shocks have also been suggested to power the luminosity of events as diverse as stellar mergers3, supernovae4 and tidal disruption events5, but observational confirmation has been lacking. Here we report simultaneous space-based optical and Îł-ray observations of the 2018 nova V906 Carinae (ASASSN-18fv), revealing a remarkable series of distinct correlated flares in both bands. The optical and Îł-ray flares occur simultaneously, implying a common origin in shocks. During the flares, the nova luminosity doubles, implying that the bulk of the luminosity is shock powered. Furthermore, we detect concurrent but weak X-ray emission from deeply embedded shocks, confirming that the shock power does not appear in the X-ray band and supporting its emergence at longer wavelengths. Our data, spanning the spectrum from radio to Îł-ray, provide direct evidence that shocks can power substantial luminosity in classical novae and other optical transients
PKS 2250â351: A Giant Radio Galaxy in Abell 3936
We present a detailed analysis of the radio galaxy PKS , a giant of 1.2 Mpc projected size, its host galaxy, and its environment. We use radio data from the Murchison Widefield Array, the upgraded Giant Metre-wavelength Radio Telescope, the Australian Square Kilometre Array Pathfinder, and the Australia Telescope Compact Array to model the jet power and age. Optical and IR data come from the Galaxy And Mass Assembly (GAMA) survey and provide information on the host galaxy and environment
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