18,372 research outputs found
Solutions of Penrose's Equation
The computational use of Killing potentials which satisfy Penrose's equation
is discussed. Penrose's equation is presented as a conformal Killing-Yano
equation and the class of possible solutions is analyzed. It is shown that
solutions exist in spacetimes of Petrov type O, D or N. In the particular case
of the Kerr background, it is shown that there can be no Killing potential for
the axial Killing vector.Comment: To appear in J. Math. Phy
Weyl-type Fields with Geodesic Lines of Force
The static electrogravitational equations are studied and it is shown that an
aligned type D metric which has a Weyl-type relationship between the
gravitational and electric potential has shearfree geodesic lines of force. All
such fields are then found and turn out to be the fields of a charged sphere,
charged infinite rod and charged infinite plate. A further solution is also
found with shearing geodesic lines of force. This new solution can have
or , but cannot be in the Majumdar-Papapetrou class (in which ). It is algebraically general and has flat equipotential surfaces.Comment: 13 pages, RevTe
Exact Nonperturbative Unitary Amplitudes for 1->N Transitions
I present an extension to arbitrary N of a previously proposed field
theoretic model, in which unitary amplitudes for processes were
obtained. The Born amplitude in this extension has the behavior
expected in a bosonic field theory. Unitarity
is violated when , or when Numerical
solutions of the coupled Schr\"odinger equations shows that for weak coupling
and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit
by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}.
The very small size of the coefficient 1/\g2 , indicative of a very weak
exponential suppression, is not in accord with standard discussions based on
saddle point analysis, which give a coefficient The weak dependence
on could have experimental implications in theories where the exponential
suppression is weak (as in this model). Non-perturbative contributions to
few-point correlation functions in this theory would arise at order $K\ \simeq\
\left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}\g2.$Comment: 11 pages, 3 figures (not included
General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
The Hamiltonian formulation of general relativity on a null surface is
established in the teleparallel geometry. No particular gauge conditons on the
tetrads are imposed, such as the time gauge condition. By means of a 3+1
decomposition the resulting Hamiltonian arises as a completely constrained
system. However, it is structurally different from the the standard
Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the
basic field quantities are tetrads that transform under the global SO(3,1) and
the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra
Stationary generalized Kerr-Schild spacetimes
In this paper we have applied the generalized Kerr-Schild transformation
finding a new family of stationary perfect-fluid solutions of the Einstein
field equations. The procedure used combines some well-known techniques of null
and timelike vector fields, from which some properties of the solutions are
studied in a coordinate-free way. These spacetimes are algebraically special
being their Petrov types II and D. This family includes all the classical
vacuum Kerr-Schild spacetimes, excepting the plane-fronted gravitational waves,
and some other interesting solutions as, for instance, the Kerr metric in the
background of the Einstein Universe. However, the family is much more general
and depends on an arbitrary function of one variable.Comment: 21 pages, LaTeX 2.09. To be published in Journal of Mathematical
Physic
Update on tests of the Cen A neutron-emission model of highest energy cosmic rays
We propose that neutron emission from Cen A dominates the cosmic ray sky at
the high end of the spectrum. Neutrons that are able to decay generate proton
diffusion fronts, whereas those that survive decay produce a spike in the
direction of the source. We use recent data reported by the Pierre Auger
Collaboration to normalize the injection spectrum and estimate the required
luminosity in cosmic rays. We find that such a luminosity, L_{CR} ~ 5 x 10^{40}
erg/s, is considerably smaller than the bolometric luminosity of Cen A, L_{bol}
~ 10^{43} erg/s. We compute the incoming current flux density as viewed by an
observer on Earth and show that the anisotropy amplitude is in agreement with
data at the 1\sigma level. Regardless of the underlying source model, our
results indicate that after a decade of data taking the Pierre Auger
Observatory will be able to test our proposal.Comment: To be published in PR
Reionization Revisited: Secondary CMB Anisotropies and Polarization
Secondary CMB anisotropies and polarization provide a laboratory to study
structure formation in the reionized epoch. We consider the kinetic
Sunyaev-Zel'dovich effect from mildly nonlinear large-scale structure and show
that it is a natural extension of the perturbative Vishniac effect. If the gas
traces the dark matter to overdensities of order 10, as expected from
simulations, this effect is at least comparable to the Vishniac effect at
arcminute scales. On smaller scales, it may be used to study the thermal
history-dependent clustering of the gas. Polarization is generated through
Thomson scattering of primordial quadrupole anisotropies, kinetic (second order
Doppler) quadrupole anisotropies and intrinsic scattering quadrupole
anisotropies. Small scale polarization results from the density and ionization
modulation of these sources. These effects generically produce comparable E and
B-parity polarization, but of negligible amplitude (0.001-0.01 uK) in adiabatic
CDM models. However, the primordial and kinetic quadrupoles are observationally
comparable today so that a null detection of B-polarization would set
constraints on the evolution and coherence of the velocity field. Conversely, a
detection of a cosmological B-polarization even at large angles does not
necessarily imply the presence of gravity waves or vorticity. For these
calculations, we develop an all-sky generalization of the Limber equation that
allows for an arbitrary local angular dependence of the source for both scalar
and symmetric trace-free tensor fields on the sky.Comment: 14 pages, 12 figures, minor changes and typo fixes reflect published
versio
Lagrangian and Hamiltonian for the Bondi-Sachs metrics
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the
Einstein vacuum equations in a closed form. Following the Dirac approach to
constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page
Completeness of Wilson loop functionals on the moduli space of and -connections
The structure of the moduli spaces \M := \A/\G of (all, not just flat)
and connections on a n-manifold is analysed. For any
topology on the corresponding spaces \A of all connections which satisfies
the weak requirement of compatibility with the affine structure of \A, the
moduli space \M is shown to be non-Hausdorff. It is then shown that the
Wilson loop functionals --i.e., the traces of holonomies of connections around
closed loops-- are complete in the sense that they suffice to separate all
separable points of \M. The methods are general enough to allow the
underlying n-manifold to be topologically non-trivial and for connections to be
defined on non-trivial bundles. The results have implications for canonical
quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-
Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
We use the canonical formalism developed together with David Robinson to st=
udy the Einstein equations on a null surface. Coordinate and gauge conditions =
are introduced to fix the triad and the coordinates on the null surface. Toget=
her with the previously found constraints, these form a sufficient number of
second class constraints so that the phase space is reduced to one pair of
canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to
both the Bondi-Sachs and the Newman-Penrose methods of studying the
gravitational field at null infinity. Asymptotic solutions in the vicinity of
null infinity which exclude logarithmic behavior require the connection to fall
off like after the Minkowski limit. This, of course, gives the previous
results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off
more slowly leads to logarithmic behavior which leaves null infinity intact,
allows for meaningful gravitational radiation, but the peeling theorem does not
extend to in the terminology of Newman-Penrose. The conclusions are in
agreement with those of Chrusciel, MacCallum, and Singleton. This work was
begun as a preliminary study of a reduced phase space for quantization of
general relativity.Comment: magnification set; pagination improved; 20 pages, plain te
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