121 research outputs found
Anti-self-dual conformal structures with null Killing vectors from projective structures
Using twistor methods, we explicitly construct all local forms of
four--dimensional real analytic neutral signature anti--self--dual conformal
structures with a null conformal Killing vector. We show that is
foliated by anti-self-dual null surfaces, and the two-dimensional leaf space
inherits a natural projective structure. The twistor space of this projective
structure is the quotient of the twistor space of by the group action
induced by the conformal Killing vector.
We obtain a local classification which branches according to whether or not
the conformal Killing vector is hyper-surface orthogonal in . We give
examples of conformal classes which contain Ricci--flat metrics on compact
complex surfaces and discuss other conformal classes with no Ricci--flat
metrics.Comment: 43 pages, 4 figures. Theorem 2 has been improved: ASD metrics are
given in terms of general projective structures without needing to choose
special representatives of the projective connection. More examples (primary
Kodaira surface, neutral Fefferman structure) have been included. Algebraic
type of the Weyl tensor has been clarified. Final version, to appear in
Commun Math Phy
Gravitational Collapse: Expanding and Collapsing Regions
We investigate the expanding and collapsing regions by taking two well-known
spherically symmetric spacetimes. For this purpose, the general formalism is
developed by using Israel junction conditions for arbitrary spacetimes. This
has been used to obtain the surface energy density and the tangential pressure.
The minimal pressure provides the gateway to explore the expanding and
collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use
the general formulation to investigate the expanding and collapsing regions of
the shell.Comment: 12 pages, 4 figures, accepted for publication in Gen. Relativ. Gra
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
Twistor geometry of a pair of second order ODEs
We discuss the twistor correspondence between path geometries in three
dimensions with vanishing Wilczynski invariants and anti-self-dual conformal
structures of signature . We show how to reconstruct a system of ODEs
with vanishing invariants for a given conformal structure, highlighting the
Ricci-flat case in particular. Using this framework, we give a new derivation
of the Wilczynski invariants for a system of ODEs whose solution space is
endowed with a conformal structure. We explain how to reconstruct the conformal
structure directly from the integral curves, and present new examples of
systems of ODEs with point symmetry algebra of dimension four and greater which
give rise to anti--self--dual structures with conformal symmetry algebra of the
same dimension. Some of these examples are analogues of plane wave
space--times in General Relativity. Finally we discuss a variational principle
for twistor curves arising from the Finsler structures with scalar flag
curvature.Comment: Final version to appear in the Communications in Mathematical
Physics. The procedure of recovering a system of torsion-fee ODEs from the
heavenly equation has been clarified. The proof of Prop 7.1 has been
expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda
Continuous image distortion by astrophysical thick lenses
Image distortion due to weak gravitational lensing is examined using a
non-perturbative method of integrating the geodesic deviation and optical
scalar equations along the null geodesics connecting the observer to a distant
source. The method we develop continuously changes the shape of the pencil of
rays from the source to the observer with no reference to lens planes in
astrophysically relevant scenarios. We compare the projected area and the ratio
of semi-major to semi-minor axes of the observed elliptical image shape for
circular sources from the continuous, thick-lens method with the commonly
assumed thin-lens approximation. We find that for truncated singular isothermal
sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens
approximation is accurate to better than 1 part in 10^4 in predicting the image
area and axes ratios. For asymmetric thick lenses consisting of two massive
clusters separated along the line of sight in redshift up to \Delta z = 0.2, we
find that modeling the image distortion as two clusters in a single lens plane
does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR
An example of localized D-branes solution on PP-wave backgrounds
In this note we provide an explicit example of type IIB supersymmetric
D3-branes solution on a pp-wave like background, consisting in the product of
an eight-dimensional pp-wave times a two-dimensional flat space. An interesting
property of our solution is the fully localization of the D3-branes (i.e. the
solution depends on all the transverse coordinates). Then we show the
generalization to other Dp-branes and to the D1/D5 system.Comment: 14 pages, 1 table; v2. references adde
Membrane Systems and Hypercomputation
We present a brief analysis of hypercomputation and its relationship
to membrane systems theory, including a re-evaluation of Turingâs
analysis of computation and the importance of timing structure,
and suggest a âcosmologicalâ variant of tissue P systems that is capable
of super-Turing behaviour. No prior technical background in hypercomputation
theory is assumed
Thinking about growth : a cognitive mapping approach to understanding small business development
School of Managemen
Spin bit models from non-planar N=4 SYM
We study spin models underlying the non-planar dynamics of SYM
gauge theory. In particular, we derive the non-local spin chain Hamiltonian
generating dilatations in the gauge theory at leading order in
but exact in .
States in the spin chain are characterized by a spin-configuration and a
linking variable describing how sites in the chain are connected. Joining and
splitting of string/traces are mimicked by a twist operator acting on the
linking variable. The results are applied to a systematic study of non-planar
anomalous dimensions and operator mixing in SYM. Intriguingly, we
identify a sequence of SYM operators for which corrections to the one-loop
anomalous dimensions stop at the first non-planar order.Comment: 22 pages, 2 figures, some typos corrected in eqs. (2.6), (2.8),
(2.11), (2.14
Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets
The spins of ten stellar black holes have been measured using the
continuum-fitting method. These black holes are located in two distinct classes
of X-ray binary systems, one that is persistently X-ray bright and another that
is transient. Both the persistent and transient black holes remain for long
periods in a state where their spectra are dominated by a thermal accretion
disk component. The spin of a black hole of known mass and distance can be
measured by fitting this thermal continuum spectrum to the thin-disk model of
Novikov and Thorne; the key fit parameter is the radius of the inner edge of
the black hole's accretion disk. Strong observational and theoretical evidence
links the inner-disk radius to the radius of the innermost stable circular
orbit, which is trivially related to the dimensionless spin parameter a_* of
the black hole (|a_*| < 1). The ten spins that have so far been measured by
this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95.
The robustness of the method is demonstrated by the dozens or hundreds of
independent and consistent measurements of spin that have been obtained for
several black holes, and through careful consideration of many sources of
systematic error. Among the results discussed is a dichotomy between the
transient and persistent black holes; the latter have higher spins and larger
masses. Also discussed is recently discovered evidence in the transient sources
for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to
appear in hard cover in the Space Sciences Series of ISSI "The Physics of
Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2,
6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405)
who find no evidence for a correlation between the power of ballistic jets
and black hole spi
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