M-Branes on k-center Instantons

We present analytic solutions for membrane metric function based on transverse $k$-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

Environmental legislation as a driver of design

and other research output

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$_{d+1}/Z_p$. 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

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

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

Inhomogeneous cosmologies, the Copernican principle and the cosmic microwave background: More on the EGS theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmological principle, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background.Comment: 17 pages; to appear in GR

SS433:the microquasar link with ULXs?

SS433 is the prototype microquasar in the Galaxy and may even be analogous to the ULX sources if the jets' kinetic energy is taken into account. However, in spite of 20 years of study, our constraints on the nature of the binary system are extremely limited as a result of the difficulty of locating spectral features that can reveal the nature and motion of the mass donor. Newly acquired, high resolution blue spectra taken when the (precessing) disc is edge-on suggest that the binary is close to a common-envelope phase, and hence providing kinematic constraints is extremely difficult. Nevertheless, we do find evidence for a massive donor, as expected for the inferred very high mass transfer rate, and we compare SS433's properties with those of Cyg X-3.Comment: 4 pages, 3 figures, to appear in "Compact binaries in the Galaxy and beyond

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 $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ 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