On some geometric features of the Kramer interior solution for a rotating perfect fluid

Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian features of the bounding surface for some rotation rates, we show, by means of a detailed analysis of the three-dimensional spatial geodesics, that the standard Newtonian convexity properties do hold. A central role is played by a family of geodesics that are introduced here, and provide a generalization of the Newtonian straight lines parallel to the axis of rotation.Comment: LaTeX, 15 pages with 4 Poscript figures. To be published in Classical and Quantum Gravit

Quasi-local contribution to the scalar self-force: Non-geodesic Motion

We extend our previous calculation of the quasi-local contribution to the self-force on a scalar particle to general (not necessarily geodesic) motion in a general spacetime. In addition to the general case and the case of a particle at rest in a stationary spacetime, we consider as examples a particle held at rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most easily analyse the effect of non-geodesic motion on our previous results and also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.

Features of gravitational waves in higher dimensions

There are several fundamental differences between four-dimensional and higher-dimensional gravitational waves, namely in the so called braneworld set-up. One of them is their asymptotic behavior within the Cauchy problem. This study is connected with the so called Hadamard problem, which aims at the question of Huygens principle validity. We investigate the effect of braneworld scenarios on the character of propagation of gravitational waves on FRW background.Comment: to appear in ERE09 proceeding

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier

In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is completely random, or unbiased. For N-level systems, the 6-level ones are the smallest for which a tomographically efficient set of N+1 mutually unbiased bases (MUBs) has not been found. To facilitate the search, we numerically extend the classification of unbiased bases, or Hadamards, by incrementally adjusting relative phases in a standard basis. We consider the non-unitarity caused by small adjustments with a second order Taylor expansion, and choose incremental steps within the 4-dimensional nullspace of the curvature. In this way we prescribe a numerical integration of a 4-parameter set of Hadamards of order 6.Comment: 5 pages, 2 figure

Gravitational Larmor formula in higher dimensions

The Larmor formula for scalar and gravitational radiation from a pointlike particle is derived in any even higher-dimensional flat spacetime. General expressions for the field in the wave zone and the energy flux are obtained in closed form. The explicit results in four and six dimensions are used to illustrate the effect of extra dimensions on linear and uniform circular motion. Prospects for detection of bulk gravitational radiation are briefly discussed.Comment: 5 pages, no figure

Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface

International audienceWe investigate numerically the axisymmetric migration of bubbles toward a free surface, using a boundary-integral technique. Our careful numerical implementation allows to study the bubble(s) deformation and film drainage; it is benchmarked against several tests. The rise of one bubble toward a free surface is studied and the computed bubble shape compared with the results of Princen [J. Colloid Interface Sci. 18, 178 (1963)]. The liquid film between the bubble and the free surface is found to drain exponentially in time in full agreement with the experimental work of Debre'geas et al. [Science 279, 1704 (1998)]. Our numerical results also cast some light on the role played by the deformation of the fluid interfaces and it turns out that for weakly deformed interfaces (high surface tension or a tiny bubble) the film drainage is faster than for a large fluid deformation. By introducing one or two additional bubble(s) below the first one, we examine to which extent the previous trends are affected by bubble-bubble interactions. For instance, for a 2-bubble chain, decreasing the bubblebubble separation increases the deformation of the last bubble in the chain. Finally, the exponential drainage of the film between the free surface and the closest bubble is preserved, yet the drainage is enhanced

Generic effective source for scalar self-force calculations

A leading approach to the modelling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic time-like geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio

Geometry of the energy landscape of the self-gravitating ring

We study the global geometry of the energy landscape of a simple model of a self-gravitating system, the self-gravitating ring (SGR). This is done by endowing the configuration space with a metric such that the dynamical trajectories are identified with geodesics. The average curvature and curvature fluctuations of the energy landscape are computed by means of Monte Carlo simulations and, when possible, of a mean-field method, showing that these global geometric quantities provide a clear geometric characterization of the collapse phase transition occurring in the SGR as the transition from a flat landscape at high energies to a landscape with mainly positive but fluctuating curvature in the collapsed phase. Moreover, curvature fluctuations show a maximum in correspondence with the energy of a possible further transition, occurring at lower energies than the collapse one, whose existence had been previously conjectured on the basis of a local analysis of the energy landscape and whose effect on the usual thermodynamic quantities, if any, is extremely weak. We also estimate the largest Lyapunov exponent $\lambda$ of the SGR using the geometric observables. The geometric estimate always gives the correct order of magnitude of $\lambda$ and is also quantitatively correct at small energy densities and, in the limit $N\to\infty$, in the whole homogeneous phase.Comment: 20 pages, 12 figure

Isolated Hadamard Matrices from Mutually Unbiased Product Bases

A new construction of complex Hadamard matrices of composite order d=pq, with primes p,q, is presented which is based on pairs of mutually unbiased bases containing only product states. For product dimensions d < 100, we illustrate the method by deriving many previously unknown complex Hadamard matrices. We obtain at least 12 new isolated matrices of Butson type, with orders ranging from 9 to 91.Comment: 21 pages, identical to published versio

A nongravitational wormhole

Using the effective metric formalism for photons in a nonlinear electromagnetic theory, we show that a certain field configuration in Born-Infeld electromagnetism in flat spacetime can be interpreted as an ultrastatic spherically symmetric wormhole. We also discuss some properties of the effective metric that are valid for any field configuration.Comment: LaTex, 9 pages with 5 figures, minor changes, accepted for publication in Class. Quantum Gra