Theoretical Aspects of the Equivalence Principle

We review several theoretical aspects of the Equivalence Principle (EP). We emphasize the unsatisfactory fact that the EP maintains the absolute character of the coupling constants of physics while General Relativity, and its generalizations (Kaluza-Klein,..., String Theory), suggest that all absolute structures should be replaced by dynamical entities. We discuss the EP-violation phenomenology of dilaton-like models, which is likely to be dominated by the linear superposition of two effects: a signal proportional to the nuclear Coulomb energy, related to the variation of the fine-structure constant, and a signal proportional to the surface nuclear binding energy, related to the variation of the light quark masses. We recall the various theoretical arguments (including a recently proposed anthropic argument) suggesting that the EP be violated at a small, but not unmeasurably small level. This motivates the need for improved tests of the EP. These tests are probing new territories in physics that are related to deep, and mysterious, issues in fundamental physics.Comment: 21 pages, no figures; submitted to a "focus issue" of Classical and Quantum Gravity on Tests of the Weak Equivalence Principle, organized by Clive Speake and Clifford Wil

Constraining the Equation of State with Moment of Inertia Measurements

We estimate that the moment of inertia of star A in the recently discovered double pulsar system PSR J0737-3039 may be determined after a few years of observation to something like 10% accuracy. This would enable accurate estimates of the radius of the star and the presure of matter in the vicinity of 1 to 2 times the nuclear saturation density, which would in turn provide strong constraints on the equation of state of neutron stars and the physics of their interiors.Comment: Submitted to ApJ, 4 figure

Post-Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits

The determination of velocities of stars from precise Doppler measurements is described here using relativistic theory of astronomical reference frames so as to determine the Keplerian and post-Keplerian parameters of binary systems. We apply successive Lorentz transformations and the relativistic equation of light propagation to establish the exact treatment of Doppler effect in binary systems both in special and general relativity theories. As a result, the Doppler shift is a sum of (1) linear in $c^{-1}$ terms, which include the ordinary Doppler effect and its variation due to the secular radial acceleration of the binary with respect to observer; (2) terms proportional to $c^{-2}$, which include the contributions from the quadratic Doppler effect caused by the relative motion of binary star with respect to the Solar system, motion of the particle emitting light and diurnal rotational motion of observer, orbital motion of the star around the binary's barycenter, and orbital motion of the Earth; and (3) terms proportional to $c^{-2}$, which include the contributions from redshifts due to gravitational fields of the star, star's companion, Galaxy, Solar system, and the Earth. After parameterization of the binary's orbit we find that the presence of periodically changing terms in the Doppler schift enables us disentangling different terms and measuring, along with the well known Keplerian parameters of the binary, four additional post-Keplerian parameters, including the inclination angle of the binary's orbit, $i$. We briefly discuss feasibility of practical implementation of these theoretical results, which crucially depends on further progress in the technique of precision Doppler measurements.Comment: Minor changes, 1 Figure included, submitted to Astrophys.

Development of ex vivo organ culture models to mimic human corneal scarring

PURPOSE: To develop ex vivo organ culture models of human corneal scarring suitable for pharmacological testing and the study of the molecular mechanisms leading to corneal haze after laser surgery or wounding. METHODS: Corneas from human donors were cultured ex vivo for 30 days, either at the air-liquid interface (AL) or immersed (IM) in the culture medium. Histological features and immunofluorescence for fibronectin, tenascin C, thrombospondin-1, and α-smooth muscle actin were graded from 0 to 3 for control corneas and for corneas wounded with an excimer laser. The effects of adding 10 ng/ml transforming growth factor-β1 (TGF-β1) to the culture medium and of prior complete removal of the epithelium and limbus, thus preventing reepithelialization, were also analyzed on wounded corneas. Collagen III expression was detected with real-time PCR. RESULTS: Wounding alone was sufficient to induce keratocyte activation and stromal disorganization, but it was only in the presence of added TGF-β1 that intense staining for fibronectin and tenascin C was found in the AL and IM models (as well as thrombospondin-1 in the AL model) and that α-smooth muscle actin became detectable. The scar-like appearance of the corneas was exacerbated when TGF-β1 was added and reepithelialization was prevented, resulting in the majority of corneas becoming opaque and marked upregulation of collagen III. CONCLUSIONS: THE MAIN FEATURES OF CORNEAL SCARRING WERE REPRODUCED IN THESE TWO COMPLEMENTARY MODELS: the AL model preserved differentiation of the epithelium and permits the topical application of active molecules, while the IM model ensures better perfusion by soluble compounds

Testing the equivalence principle: why and how?

Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. One introduces a simplified rationale based on a trichotomy of competing classes of theoretical models.Comment: 11 pages, Latex, uses ioplppt.sty, submitted to Class. Quantum Gra

Spontaneous Scalarization and Boson Stars

We study spontaneous scalarization in Scalar-Tensor boson stars. We find that scalarization does not occur in stars whose bosons have no self-interaction. We introduce a quartic self-interaction term into the boson Lagrangian and show that when this term is large, scalarization does occur. Strong self-interaction leads to a large value of the compactness (or sensitivity) of the boson star, a necessary condition for scalarization to occur, and we derive an analytical expression for computing the sensitivity of a boson star in Brans-Dicke theory from its mass and particle number. Next we comment on how one can use the sensitivity of a star in any Scalar-Tensor theory to determine how its mass changes when it undergoes gravitational evolution. Finally, in the Appendix, we derive the most general form of the boson wavefunction that minimises the energy of the star when the bosons carry a U(1) charge.Comment: 23 pages, 5 postscript figures. Typing errors corrected. Includes some new text that relates the paper to several previous results. Accepted for publication in PR

Self-accelerated Universe

It is widely believed that the large redshifts for distant supernovae are explained by the vacuum energy dominance, or, in other words, by the cosmological constant in Einstein's equations, which is responsible for the anti-gravitation effect. A tacit assumption is that particles move along a geodesic for the background metric. This is in the same spirit as the consensus regarding the uniform Galilean motion of a free electron. However, there is a runaway solution to the Lorentz--Dirac equation governing the behavior of a radiating electron, in addition to the Galilean solution. Likewise, a runaway solution to the entire system of equations, both gravitation and matter equations of motion including, may provide an alternative explanation for the accelerated expansion of the Universe, without recourse to the hypothetic cosmological constant.Comment: 11 pages; Talk at the 9th Adriatic Meeting, Dubrovnic, Croatia, 4-14 September, 2003, Minor improvement, references added; to appear in ``Progress in General Relativity and Quantum Cosmology Research'', Nova Science Publisher

Pulse Arrival-Times from Binary Pulsars with Rotating Black Hole Companions

We present a study of the gravitational time delay of arrival of signals from binary pulsar systems with rotating black hole companions. In particular, we investigate the strength of this effect (Shapiro delay) as a function of the inclination, eccentricity and period of the orbit, as well as the mass and angular momentum of the black hole. This study is based on direct numerical integration of null geodesics in a Kerr background geometry. We find that, for binaries with sufficiently high orbital inclinations ($> 89^o$) and compact companion masses $> 10 M_\odot$, the effect arising from the rotation of the black hole in the system amounts to a microsecond-level variation of the arrival times of the pulsar pulses. If measurable, this variation could provide a unique signature for the presence of a rotating black hole in a binary pulsar system.Comment: 8 pages, 1 figur

Time-symmetric initial data for binary black holes in numerical relativity

We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-Newtonian metric up to the 2PN order. It represents a non-linear deformation of the solution of Brill and Lindquist, i.e. an asymptotically flat region is connected to two asymptotically flat (in a certain weak sense) sheets, that are the images of the two singularities through appropriate inversion transformations. The total ADM mass M as well as the individual masses m_1 and m_2 (when they exist) are computed by surface integrals performed at infinity. Using second order perturbation theory on the Brill-Lindquist background, we prove that the binary's interacting mass-energy M-m_1-m_2 is well-defined at the 2PN order and in agreement with the known post-Newtonian result.Comment: 27 pages, to appear in Phys. Rev.

Einstein billiards and spatially homogeneous cosmological models

In this paper, we analyse the Einstein and Einstein-Maxwell billiards for all spatially homogeneous cosmological models corresponding to 3 and 4 dimensional real unimodular Lie algebras and provide the list of those models which are chaotic in the Belinskii, Khalatnikov and Lifschitz (BKL) limit. Through the billiard picture, we confirm that, in D=5 spacetime dimensions, chaos is present if off-diagonal metric elements are kept: the finite volume billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. The most generic cases bring in the same algebras as in the inhomogeneous case, but other algebras appear through special initial conditions.Comment: 27 pages, 10 figures, additional possibility analysed in section 4.3, references added, typos correcte