The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries

This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the timelike boundary $\cal B$ orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples.Comment: 23 pages, 1 figure, LaTeX. The action is altered to include a corner term which results in a different value for the non-orthogonal term. An additional appendix with Euclidean results is included. To appear in Class. Quant. Gra

Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism

We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation - joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit.Comment: Minor LaTeX error corrected. GRjunction for GRTensorII is available from http://astro.queensu.ca/~grtensor/GRjunction.htm

Stability of Transparent Spherically Symmetric Thin Shells and Wormholes

The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations.Comment: 12 pages, 7 figures, revtex. Final form to appear in Phys. Rev.

Lax pair tensors in arbitrary dimensions

A recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and coupling-constant metamorphosis to obtain a geometric Lax formulation. We also exploit the results to construct integrable spacetimes, satisfying the weak energy condition.Comment: 8 pages, uses IOP style files. Minor correction. Submitted to J. Phys

Double-bounce domain-wall in Einstein-Yang-Mills-Scalar black holes

We find Einstein-Yang-Mills (EYM) black hole solutions endowed with massless scalar hair in the presence of a potential $V\left(\phi \right)$ as function of the scalar field $\phi$. Choosing $V\left(\phi \right) =$constant (or zero) sets the scalar field to vanish leaving us with the EYM black holes. Our class of black hole solutions is new so that they do not asymptote in general to any known limits. Particular case is given, however, which admits an asymptotically anti de Sitter limit in $6-$dimensional spacetime. The role of the potential $V\left(\phi \right)$ in making double bounces (i.e. both a minimum and maximum radii) on a Domain Wall (DW) universe is highlighted.Comment: 9 pages, 1 figure, final version for publication in EPJ

Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.

All static spherically symmetric perfect fluid solutions of Einstein's Equations

An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by non-trivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions.Comment: Final form to appear in Phys Rev D. Includes a number of clarification

The Application of the Newman-Janis Algorithm in Obtaining Interior Solutions of the Kerr Metric

In this paper we present a class of metrics to be considered as new possible sources for the Kerr metric. These new solutions are generated by applying the Newman-Janis algorithm (NJA) to any static spherically symmetric (SSS) ``seed'' metric. The continuity conditions for joining any two of these new metrics is presented. A specific analysis of the joining of interior solutions to the Kerr exterior is made. The boundary conditions used are those first developed by Dormois and Israel. We find that the NJA can be used to generate new physically allowable interior solutions. These new solutions can be matched smoothly to the Kerr metric. We present a general method for finding such solutions with oblate spheroidal boundary surfaces. Finally a trial solution is found and presented.Comment: 11 pages, Latex, 4 postscript figures. To be published in Classical and Quantum Gravity. Title and abstract are now on the same pag

Superposition of Weyl solutions: The equilibrium forces

Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The force on the strut like singularities is computed for a variety of situations. The superposition of a ring and a particle is studied in some detailComment: 31 pages, 7 figures, psbox macro. Submitted to Classical and Quantum Gravit

New measurement of the scattering cross section of slow neutrons on liquid parahydrogen from neutron transmission

Liquid hydrogen is a dense Bose fluid whose equilibrium properties are both calculable from first principles using various theoretical approaches and of interest for the understanding of a wide range of questions in many body physics. Unfortunately, the pair correlation function $g(r)$ inferred from neutron scattering measurements of the differential cross section $d\sigma \over d\Omega$ from different measurements reported in the literature are inconsistent. We have measured the energy dependence of the total cross section and the scattering cross section for slow neutrons with energies between 0.43~meV and 16.1~meV on liquid hydrogen at 15.6~K (which is dominated by the parahydrogen component) using neutron transmission measurements on the hydrogen target of the NPDGamma collaboration at the Spallation Neutron Source at Oak Ridge National Laboratory. The relationship between the neutron transmission measurement we perform and the total cross section is unambiguous, and the energy range accesses length scales where the pair correlation function is rapidly varying. At 1~meV our measurement is a factor of 3 below the data from previous work. We present evidence that these previous measurements of the hydrogen cross section, which assumed that the equilibrium value for the ratio of orthohydrogen and parahydrogen has been reached in the target liquid, were in fact contaminated with an extra non-equilibrium component of orthohydrogen. Liquid parahydrogen is also a widely-used neutron moderator medium, and an accurate knowledge of its slow neutron cross section is essential for the design and optimization of intense slow neutron sources. We describe our measurements and compare them with previous work.Comment: Edited for submission to Physical Review