R-Modes in Superfluid Neutron Stars

The analogs of r-modes in superfluid neutron stars are studied here. These modes, which are governed primarily by the Coriolis force, are identical to their ordinary-fluid counterparts at the lowest order in the small angular-velocity expansion used here. The equations that determine the next order terms are derived and solved numerically for fairly realistic superfluid neutron-star models. The damping of these modes by superfluid ``mutual friction'' (which vanishes at the lowest order in this expansion) is found to have a characteristic time-scale of about 10^4 s for the m=2 r-mode in a ``typical'' superfluid neutron-star model. This time-scale is far too long to allow mutual friction to suppress the recently discovered gravitational radiation driven instability in the r-modes. However, the strength of the mutual friction damping depends very sensitively on the details of the neutron-star core superfluid. A small fraction of the presently acceptable range of superfluid models have characteristic mutual friction damping times that are short enough (i.e. shorter than about 5 s) to suppress the gravitational radiation driven instability completely.Comment: 15 pages, 8 figure

The metaphysics of Machian frame-dragging

The paper investigates the kind of dependence relation that best portrays Machian frame-dragging in general relativity. The question is tricky because frame-dragging relates local inertial frames to distant distributions of matter in a time-independent way, thus establishing some sort of non-local link between the two. For this reason, a plain causal interpretation of frame-dragging faces huge challenges. The paper will shed light on the issue by using a generalized structural equation model analysis in terms of manipulationist counterfactuals recently applied in the context of metaphysical enquiry by Schaffer (2016) and Wilson (2017). The verdict of the analysis will be that frame-dragging is best understood in terms of a novel type of dependence relation that is half-way between causation and grounding

Governance, Coordination and Evaluation: the case for an epistemological focus and a return to C.E. Lindblom

While much political science research focuses on conceptualizing and analyzing various forms of governance, there remains a need to develop frameworks and criteria for governance evaluation (Torfing et al 2012). The post-positivist turn, influential in recent governance theory, emphasizes the complexity, uncertainty and the contested normative dimensions of policy analysis. Yet a central evaluative question still arises concerning the capacity of governance networks to facilitate ‘coordination’. The classic contributions of Charles Lindblom, although pre-dating the contemporary governance literature, can enable further elaboration of and engagement with this question. Lindblom’s conceptualisation of coordination challenges in the face of complexity shares with post-positivism a recognition of the inevitably contested nature of policy goals. Yet Lindblom suggests a closer focus on the complex, dynamically evolving, broadly ‘economic’ choices and trade-offs involved in defining and delivery policy for enabling these goals to be achieved and the significant epistemological challenges that they raise for policy-makers. This focus can complement and enrich both post-positivist scholarship and the process and incentives-orientated approaches which predominate in contemporary political science research on coordination in governance. This is briefly illustrated through a short case study evaluating governance for steering markets towards delivering low and zero carbon homes in England

Testing outer boundary treatments for the Einstein equations

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections.Comment: Modified to agree with version accepted for publication in Class. Quantum Gra

Reducing orbital eccentricity in binary black hole simulations

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQ

Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds.Comment: 11 page

Improved outer boundary conditions for Einstein's field equations

In a recent article, we constructed a hierarchy B_L of outer boundary conditions for Einstein's field equations with the property that, for a spherical outer boundary, it is perfectly absorbing for linearized gravitational radiation up to a given angular momentum number L. In this article, we generalize B_2 so that it can be applied to fairly general foliations of spacetime by space-like hypersurfaces and general outer boundary shapes and further, we improve B_2 in two steps: (i) we give a local boundary condition C_2 which is perfectly absorbing including first order contributions in 2M/R of curvature corrections for quadrupolar waves (where M is the mass of the spacetime and R is a typical radius of the outer boundary) and which significantly reduces spurious reflections due to backscatter, and (ii) we give a non-local boundary condition D_2 which is exact when first order corrections in 2M/R for both curvature and backscatter are considered, for quadrupolar radiation.Comment: accepted Class. Quant. Grav. numerical relativity special issue; 17 pages and 1 figur

Solving the Darwin problem in the first post-Newtonian approximation of general relativity

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.Comment: 33 pages, revtex, 4 figures(eps), accepted for publication in Phys. Rev.