Chebyshev constants for the unit circle

It is proven that for any system of n points z_1, ..., z_n on the (complex) unit circle, there exists another point z of norm 1, such that $$\sum 1/|z-z_k|^2 \leq n^2/4.$$ Equality holds iff the point system is a rotated copy of the nth unit roots. Two proofs are presented: one uses a characterisation of equioscillating rational functions, while the other is based on Bernstein's inequality.Comment: 11 page

On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case

The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum space-times containing spatial hypersurfaces with cosmological symmetries. This theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is not a representant of the above class, but contains the static Einstein brane as embedded hypersurface. We prove that the 5d Birkhoff theorem is still satisfied in a weaker sense: the GM space-time is related to the degenerated horizon metric of certain black-hole space-times of the allowed class. This result resembles the connection between the Bertotti-Robinson space-time and the horizon region of the extremal Reissner-Nordstrom space-time in general relativity.Comment: 13 pages; v2: title amended, to be published in Classical and Quantum Gravit

Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction

The radiation reaction in compact spinning binaries on eccentric orbits due to the quadrupole-monopole interaction is studied. This contribution is of second post-Newtonian order. As result of the precession of spins the magnitude $L$ of the orbital angular momentum is not conserved. Therefore a proper characterization of the perturbed radial motion is provided by the energy $E$ and angular average $\bar{L}$. As powerful computing tools, the generalized true and eccentric anomaly parametrizations are introduced. Then the secular losses in energy and magnitude of orbital angular momentum together with the secular evolution of the relative orientations of the orbital angular momentum and spins are found for eccentric orbits by use of the residue theorem. The circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.

Bose-Einstein Condensate Dark Matter Halos confronted with galactic rotation curves

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range.The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power.Comment: published versio

A Spherically Symmetric Closed Universe as an Example of a 2D Dilatonic Model

We study the two-dimensional (2D) dilatonic model describing a massless scalar field minimally coupled to the spherically reduced Einstein-Hilbert gravity. The general solution of this model is given in the case when a Killing vector is present. When interpreted in four dimensions, the solution describes either a static or a homogeneous collision of incoming and outgoing null dust streams with spherical symmetry. The homogeneous Universe is closed.Comment: 5 pages, 2 figures, to appear in Physical Review

Friedmann branes with variable tension

We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by E\"otv\"os. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a Friedmann brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter space-time.Comment: 12 pages, to appear in Phys. Rev.

Do 18-month-olds really attribute mental states to others? A critical test

In the research reported here, we investigated whether 18-month-olds would use their own past experience of visual access to attribute perception and consequent beliefs to other people. Infants in this study wore either opaque blindfolds (opaque condition) or trick blindfolds that looked opaque but were actually transparent (trick condition). Then both groups of infants observed an actor wearing one of the same blindfolds that they themselves had experienced, while a puppet removed an object from its location. Anticipatory eye movements revealed that infants who had experienced opaque blindfolds expected the actor to behave in accordance with a false belief about the object's location, but that infants who had experienced trick blindfolds did not exhibit that expectation. Our results suggest that 18-month-olds used self-experience with the blindfolds to assess the actor's visual access and to update her belief state accordingly. These data constitute compelling evidence that 18-month-olds infer perceptual access and appreciate its causal role in altering the epistemic states of other people

The luminosity-redshift relation in brane-worlds: I. Analytical results

The luminosity distance - redshift relation is analytically given for generalized Randall-Sundrum type II brane-world models containing dark radiation. The derived expressions contain both elementary functions and elliptic integrals of the first and second kind. First we derive the relation for models with the Randall-Sundrum fine-tuning. Then we generalize the method for models with cosmological constant. The analytical results are suitable for testing brane-world models when future supernova data at higher redshifts will be available.Comment: v2: Improved discussion and new references; analytical results kept, comparison with observation moved to astro-ph/0702610, 18 pages, 2 figures v3: Minor improvements, few new references. Version to appear in the initial issue of PMC Physics