Mach's principle, according to which the origin of gravitational interaction depends on the presence of all the masses in the universe, was expressed in a quantitative form by Sciama (1953). Since this idea suggests a variable speed of light (VSL), it is shown here that the arising variability of c is in agreement with all GR tests regarding time and length scales which are subject to variation as well. Moreover, VSL opens the possibility to write the total energy of a particle as E=mc^2; this necessarily leads to the proportionality of inertial and gravitating mass, the equivalence principle. Furthermore, a formula for c depending on the mass distribution is given that reproduces Newtons law of gravitation. This mass distribution allows to calculate a slightly variable term that corresponds to the `constant' G. The present proposal may also supply an alternative explanation to the flatness problem and the horizon problem in cosmology.

In this paper we study long distance modifications of gravity obtained by considering actions that are singular in the limit of vanishing curvature. In particular, we showed in a previous publication that models that include inverse powers of curvature invariants that diverge for r->0 in the Schwarzschild geometry, recover an acceptable weak field limit at short distances from sources. We study then the linearisation of generic actions of the form L=F[R,P,Q] where P=R_{ab}R^{ab} and Q=R_{abcd}R^{abcd}. We show that for the case in which F[R,P,Q]=F[R,Q-4P], the theory is ghost free. Assuming this is the case, in the models that can explain the acceleration of the Universe without recourse to Dark Energy there is still an extra scalar field in the spectrum besides the massless spin two graviton. The mass of this extra excitation is of the order of the Hubble scale in vacuum. We nevertheless recover Einstein gravity at short distances because the mass of this scalar field depends on the background in such a way that it effectively decouples when one gets close to any source. Remarkably, for the values of the parameters necessary to explain the cosmic acceleration the induced modifications of gravity are suppressed at the Solar System level but can be important for systems like a galaxy.

The process of $\nu\bar{\nu}$ radiation from a relativistic plasma of electrons and positrons is studied within the Random Phase Approximation. We show that the electromagnetic interactions among the plasma particles crucially modify the neutrino radiation caused by $e^{+}e^{-}$ annihilation, due to screening of the electron vector weak coupling with the neutrino field. As a result, the corresponding contribution to the total neutrino energy losses from the plasma is strongly suppressed. However, the vector weak coupling manifests itself in a new feature, by causing $\nu\bar{\nu}$ decays of off-shell photons. The well-known $\nu\bar{\nu}$ decays of the transverse and longitudinal on-shell plasmons are also reproduced in the approximation used.

We discuss the validity and the outcome of a scaling hypothesis proposed by us some years ago, according to which the influence of the density on the slowing down of flow and relaxation in glassforming liquids and polymers is described trough a single effective interaction energy Einf(rho). We stress the formal consequences and the physical meaning of the scaling.

On the basis of Galilean invariance and the Doppler formula, combined with an observational condition, it is shown that the constancy of the velocity of light {\it in vacuo} can be derived, together with time-dilatation and Lorentz contraction. It is not necessary to take the constancy as a postulate.

The dynamic structure factor of a simple relativistic fluid is calculated. The coupling of acceleration with the heat flux present in Eckart's version of irreversible relativistic thermodynamics is examined using the Rayleigh-Brillouin spectrum of the fluid. A modification of the width of the Rayleigh peak associated to Eckart's picture of the relativistic nature of heat is predicted and estimated.

Non-minimal gauge models with exact unbroken improper space-time symmetries are constructed and their cosmological and astrophysical implications explored.

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.

Nuclear structure of 7Be, 8B and 7,8Li is studied within the ab initio no-core shell model (NCSM). Starting from the high-precision CD-Bonn 2000 nucleon-nucleon (NN) interaction, wave functions of 7Be and 8B bound states are obtained in basis spaces up to 10 hbar Omega and used to calculate channel cluster form factors (overlap integrals) of the 8B ground state with 7Be+p. Due to the use of the harmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic properties. We fix this problem in two alternative ways. First, by a Woods-Saxon (WS) potential solution fit to the interior of the NCSM overlap integrals. Second, by a direct matching with the Whittaker function. The corrected overlap integrals are then used for the 7Be(p,gamma)8B S-factor calculation. We study the convergence of the S-factor with respect to the NCSM HO frequency and the model space size. Our S-factor results are in agreement with recent direct measurement data.

The cosmological constant sets certain scales important in cosmology. We show that \Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical applications. Of special interest is the extension of orbits and velocity of test particles traveling over Mpc distances. We will show that there exists a lower and an upper cut-off on the possible velocities of test particles. For a test body moving in a central gravitational field \Lambda enforces a maximal value of the angular momentum if we insist on bound orbits of the test body which move at a distance larger than the Schwarzschild radius.

We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.

The most precise measurements are done at present by timing of radiopulsars in binary systems with two neutron stars. The timing measurements of the Taylor-Hulse pulsar give the most precise results on testing of general relativity (GR), finding implicit proof of existence of gravitational waves. We show that the existing measurements, used for checking the variability of the fundamental constants, give the upper limit for the variation of the gravitational constant ${\dot G}/{G}=(4.3\pm 4.9)\cdot 10^{-12}$ year{$^{-1}$}. Timing measurements of the binary pulsar J0737-3039 undoubtfully should give more precise results in the nearest future.

We determine the general conditions for the existence of Godel, Einstein static, and de Sitter universes in gravity theories derived from a Lagrangian that is an arbitrary function of the scalar curvature and Ricci and Riemann curvature invariants. Explicit expressions for the solutions are found in terms of the parameters defining the Lagrangian. We also determine the conditions on the Lagrangian of the theory under which time-travel is allowed in the Godel universes.

We present a comprehensive study of TeV black hole events in Earth's atmosphere originated by cosmic rays of very high energy. An advanced fortran Monte Carlo code is developed and used to simulate black hole extensive air showers from ultrahigh-energy neutrino-nucleon interactions. We investigate the characteristics of these events, compare the black hole air showers to standard model air showers, and test different theoretical and phenomenological models of black hole formation and evolution. The main features of black hole air showers are found to be independent of the model considered. No significant differences between models are likely to be observed at fluorescence telescopes and/or ground arrays. We also discuss the tau ``double bang'' signature in black hole air showers. We find that the energy deposited in the second bang is too small to produce a detectable peak. Our results show that the theory of TeV-scale black holes in ultrahigh-energy cosmic rays leads to robust predictions, but the fine prints of new physics are hardly to be investigated through atmospheric black hole events in the near future.

Isomeric states in the nuclei along the rapid proton capture process path are studied by the projected shell model. Emphasis is given to two waiting point nuclei Se-68 and Kr-72 that are characterized by shape coexistence. Energy surface calculations indicate that the ground state of these nuclei corresponds to an oblate-deformed minimum, while the lowest state at the prolate-deformed minimum can be considered as a shape isomer. Due to occupation of the orbitals with large K-components, states built upon two-quasiparticle excitations at the oblate-deformed minimum may form high $K$-isomers. The impact of the isomer states on isotopic abundance in X-ray bursts is studied in a multi-mass-zone X-ray burst model by assuming an upper-lower limit approach.

Black holes acting as gravitational lenses produce, besides the primary and secondary weak field images, two infinite sets of relativistic images. These images can be studied using the strong field limit, an analytic method based on a logarithmic asymptotic approximation of the deflection angle. In this work, braneworld black holes are analyzed as gravitational lenses in the strong field limit and the feasibility of observation of the images is discussed.

In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning bodies is developed and spin-orbit, spin-spin and quadrupole-spin Hamiltonians are found at leading order. The existence of tidal, as well as self induced finite size effects is shown, and the contribution to the Hamiltonian is calculated in the latter. It is shown that tidal deformations start formally at O(v^6) and O(v^10) for maximally rotating general and compact objects respectively, whereas self induced effects can show up at leading order. Agreement is found for the cases where the results are known.

In this paper, charged black holes in general relativity coupled to Born-Infeld electrodynamics are studied as gravitational lenses. The positions and magnifications of the relativistic images are obtained using the strong deflection limit, and the results are compared with those corresponding to a Reissner-Nordstrom black hole with the same mass and charge. The model is applied to the Galactic center black hole.

We show that the inclusion of backreaction of massive long wavelengths imposes dynamical constraints on the allowed phase space of initial conditions for inflation. Only high energy inflation is stable against collapse from the gravitational instability of massive perturbations. The backreaction term in the Wheeler-DeWitt equation, for the wavefunction of the universe propagating on the landscape background, originates from the self-gravity of massive moduli degrees of freedom and metric perturbations and leads to a Master equation.
We present arguments to lend support to the conjecture that the initial conditions problem can not be meaningfully addressed by thermostatistics where gravitational degrees of freedom are concerned. The choice of the initial conditions for the universe in the phase space and the emergence of an arrow of time have to be treated as a dynamic selection.

We investigate the Selection of Original Universe Proposal (SOUP) of Tye et al. and show that as it stands, this proposal is flawed. The corrections to the Euclidean gravity action that were to select a Universe with a sufficiently large value of the cosmological constant $\Lambda$ to allow for an inflationary phase, only serve to {\it renormalize} the cosmological constant so that $\Lambda \to \Lambda_{\rm eff}$, thereby reintroducing the issue of how to select the initial conditions allowing for inflation in the early Universe.

We derive a long wavelength effective point particle description of four-dimensional Schwarzschild black holes. In this effective theory, absorptive effects are incorporated by introducing degrees of freedom localized on the worldline that mimic the interaction between the horizon and bulk fields. The correlation functions of composite operators in this worldline theory can be obtained by standard matching calculations. For example, we obtain the low frequency two-point function of multipole worldline operators by relating them to the long wavelength graviton black hole absorptive cross section. The effective theory is then used to predict the leading effects of absorption in several astrophysically motivated examples, including the dynamics of non-relativistic black hole binary inspirals and the motion of a small black hole in an arbitrary background geometry. Our results can be written compactly in terms of absorption cross sections, and can be easily applied to the dissipative dynamics of any compact object, e.g. neutron stars. The relation of our methodology to that developed in the context of the AdS/CFT correspondence is discussed.

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

A recent paper by Hsu & Zee (physics/0510102) suggests that if a Creator wanted to leave a message for us, and she wanted it to be decipherable to all sentient beings, then she would place it on the most cosmic of all billboards, the Cosmic Microwave Background (CMB) sky. Here we point out that the spherical harmonic coefficients of the observed CMB anisotropies (or their squared amplitudes at each multipole) depend on the location of the observer, in both space and time. The amount of observer-independent information available in the CMB is a small fraction of the total that any observer can measure. Hence a lengthy message on the CMB sky is fundamentally no less observer-specific than a communication hidden in this morning's tea-leaves. Nevertheless, the CMB sky does encode a wealth of information about the structure of the cosmos and possibly about the nature of physics at the highest energy levels. The Universe has left us a message all on its own.

Cooperstock and Tieu have proposed a model to account for galactic rotation curves without invoking dark matter. I argue that no model of this type can work.

The non-abelian Einstein-Born-Infeld-Dilaton theory, which rules the dynamics of tensor-scalar gravitation coupled to a $su(2)$-valued gauge field ruled by Born-Infeld lagrangian, is studied in a cosmological framework. The microscopic energy exchange between the gauge field and the dilaton which results from a non-universality of the coupling to gravity modifies the usual behaviour of tensor-scalar theories coupled to matter fluids. General cosmological evolutions are derived for different couplings to gravitation and a comparison to universal coupling is highlighted. Evidences of cosmic acceleration are presented when the evolution is interpreted in the Jordan physical frame of a matter respecting the weak equivalence principle. The importance for the mechanism of cosmic acceleration of the dynamics of the Born-Infeld gauge field, the attraction role of the matter fluid and the non-universality of the gravitational couplings is briefly outlined.

We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k. Orbifold singularities of this space correspond to coincident vortices and are resolved resulting in a smooth moduli manifold. Relation to Kahler quotient construction is discussed.

The present works complements and expands a previous one, focused on the emission of scalar fields by a (4+n)-dimensional rotating black hole on the brane, by studying the emission of gauge fields on the brane from a similar black hole. A comprehensive analysis of the particle, energy and angular momentum emission rates is undertaken, for arbitrary angular momentum of the black hole and dimensionality of spacetime. Our analysis reveals the existence of a number of distinct features associated with the emission of spin-1 fields from a rotating black hole on the brane, such as the behaviour and magnitude of the different emission rates, the angular distribution of particles and energy, the relative enhancement compared to the scalar fields, and the magnitude of the superradiance effect. Apart from their theoretical interest, these features can comprise clear signatures of the emission of Hawking radiation from a brane-world black hole during its spin-down phase upon successful detection of this effect during an experiment.