5,861 research outputs found
Soliton Solutions to the Einstein Equations in Five Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,
with the added feature of having Lorentzian signatures. They provide an
affirmative answer to the open question as to whether or not there exist
solutions with negative cosmological constant that asymptotically approach
AdS, but have less energy than AdS. We present
evidence that these solutions are the lowest-energy states within their
asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title
changed by journal from original title "Eguchi-Hanson Solitons
M-Branes on k-center Instantons
We present analytic solutions for membrane metric function based on
transverse -center instanton geometries. The membrane metric functions
depend on more than two transverse coordinates and the solutions provide
realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections.
All solutions have partial preserved supersymmetries.Comment: 22 pages, 5 figure
Locally extracting scalar, vector and tensor modes in cosmological perturbation theory
Cosmological perturbation theory relies on the decomposition of perturbations
into so-called scalar, vector and tensor modes. This decomposition is non-local
and depends on unknowable boundary conditions. The non-locality is particularly
important at second- and higher-order because perturbative modes are sourced by
products of lower-oder modes, which must be integrated over all space in order
to isolate each mode. However, given a trace-free rank-2 tensor, a locally
defined scalar mode may be trivially derived by taking two divergences, which
knocks out the vector and tensor degrees of freedom. A similar local
differential operation will return a pure vector mode. This means that scalar
and vector degrees of freedom have local descriptions. The corresponding local
extraction of the tensor mode is unknown however. We give it here. The
operators we define are useful for defining gauge-invariant quantities at
second-order. We perform much of our analysis using an index-free
`vector-calculus' approach which makes manipulating tensor equations
considerably simpler.Comment: 13 pages. Final version to appear in CQ
Eguchi-Hanson Solitons in Odd Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added
feature of having Lorentzian signatures. They are asymptotic to
(A)dS. In the AdS case their energy is negative relative to that of
pure AdS. We present perturbative evidence in 5 dimensions that such metrics
are the states of lowest energy in their asymptotic class, and present a
conjecture that this is generally true for all such metrics. In the dS case
these solutions have a cosmological horizon. We show that their mass at future
infinity is less than that of pure dS.Comment: 26 pages, Late
Delocalization of brane gravity by a bulk black hole
We investigate the analogue of the Randall-Sundrum brane-world in the case
when the bulk contains a black hole. Instead of the static vacuum Minkowski
brane of the RS model, we have an Einstein static vacuum brane. We find that
the presence of the bulk black hole has a dramatic effect on the gravity that
is felt by brane observers. In the RS model, the 5D graviton has a stable
localized zero-mode that reproduces 4D gravity on the brane at low energies.
With a bulk black hole, there is no such solution -- gravity is delocalized by
the 5D horizon. However, the brane does support a discrete spectrum of
metastable massive bound states, or quasinormal modes, as was recently shown to
be the case in the RS scenario. These states should dominate the high frequency
component of the bulk gravity wave spectrum on a cosmological brane. We expect
our results to generalize to any bulk spacetime containing a Killing horizon.Comment: 7 pages, 6 figure
A generalized linear Hubble law for an inhomogeneous barotropic Universe
In this work, I present a generalized linear Hubble law for a barotropic
spherically symmetric inhomogeneous spacetime, which is in principle compatible
with the acceleration of the cosmic expansion obtained as a result of high
redshift Supernovae data. The new Hubble function, defined by this law, has two
additional terms besides an expansion one, similar to the usual volume
expansion one of the FLRW models, but now due to an angular expansion. The
first additional term is dipolar and is a consequence of the existence of a
kinematic acceleration of the observer, generated by a negative gradient of
pressure or of mass-energy density. The second one is quadrupolar and due to
the shear. Both additional terms are anisotropic for off-centre observers,
because of to their dependence on a telescopic angle of observation. This
generalized linear Hubble law could explain, in a cosmological setting, the
observed large scale flow of matter, without to have recourse to peculiar
velocity-type newtonian models. It is pointed out also, that the matter dipole
direction should coincide with the CBR dipole one.Comment: 9 pages, LaTeX, to be published in Class. Quantum Gra
Symmetries of a class of nonlinear fourth order partial differential equations
In this paper we study symmetry reductions of a class of nonlinear fourth
order partial differential equations \be u_{tt} = \left(\kappa u + \gamma
u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2,
\ee where , , , and are constants. This
equation may be thought of as a fourth order analogue of a generalization of
the Camassa-Holm equation, about which there has been considerable recent
interest. Further equation (1) is a ``Boussinesq-type'' equation which arises
as a model of vibrations of an anharmonic mass-spring chain and admits both
``compacton'' and conventional solitons. A catalogue of symmetry reductions for
equation (1) is obtained using the classical Lie method and the nonclassical
method due to Bluman and Cole. In particular we obtain several reductions using
the nonclassical method which are no} obtainable through the classical method
Non-classical symmetries and the singular manifold method: A further two examples
This paper discusses two equations with the conditional Painleve property.
The usefulness of the singular manifold method as a tool for determining the
non-classical symmetries that reduce the equations to ordinary differential
equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics
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