It is an early result of electrostatics in curved space that the gravitational mass of a charge distribution changes by an amount equal to $U_{\mathrm{es}}/c^2$, where $U_{\mathrm{es}}$ is the internal electrostatic potential energy and $c$ is the speed of light, if the system is supported at rest by external forces. This fact, independently rediscovered in recent years in the case of a simple dipole, confirms a very reasonable expectation grounded in the mass-energy equivalency equation. However, it is an unsolved paradox of classical electrodynamics that the renormalized mass of an accelerated dipole calculated from the self-forces due to the distortion of the Coulomb field differs in general from that expected from the energy correction, $U_{\mathrm{es}}/c^2$, unless the acceleration is transversal to the orientation of the dipole. Here we show that this apparent paradox disappears for any dipole orientation if the self-force is evaluated by means of Whittaker’s exact solution for the field of the single charge in a homogeneous gravitational field described in the Rindler metric. The discussion is supported by computer algebra results, diagrams of the electric fields distorted by gravitation, and a brief analysis of the prospects for realistic experimentation. The gravitational correction to dipole-dipole interactions is also discussed.

Gravitational lensing is investigated in the weak field limit of fourth order gravity in which the Lagrangian of the gravitational field is modified by replacing the Ricci scalar curvature $R$ with an analytical expression $f(R)$. Considering the case of a pointlike lens, we study the behavior of the deflection angle in the case of power-law Lagrangians, i.e. with $f(R)\propto R^n$. In order to investigate possible detectable signatures, the position of the Einstein ring and the solutions of the lens equation are evaluated considering the change with respect to the standard case. Effects on the amplification of the images and the Paczynski curve in microlensing experiments are also estimated.

In the framework of thermal quantization of radial geodesics completely confined behind the horizons we calculate the entropy of BTZ black hole in agreement with the Bekenstein-Hawking relation. Particles in the BTZ black hole occupy the only quantum ground level. The quantization allows us to find a linear dependence of black hole mass versus its orbital momentum.

We present a perturbative treatment of the evolution under their mutual self-gravity of particles displaced off an infinite perfect lattice, both for a static space and for a homogeneously expanding space as in cosmological $N$-body simulations. The treatment, analogous to that of perturbations to a crystal in solid state physics, can be seen as a discrete (i.e. particle) generalization of the perturbative solution in the Lagrangian formalism of a self-gravitating fluid. Working to linear order, we show explicitly that this fluid evolution is recovered in the limit that the initial perturbations are restricted to modes of wavelength much larger than the lattice spacing. The full spectrum of eigenvalues of the simxple cubic lattice contains both oscillatory modes and unstable modes which grow slightly faster than in the fluid limit. A detailed comparison of our perturbative treatment, at linear order, with full numerical simulations is presented, for two very different classes of initial perturbation spectra. We find that the range of validity is similar to that of the perturbative fluid approximation (i.e. up to close to “shell-crossing”), but that the accuracy in tracing the evolution is superior. The formalism provides a powerful tool to systematically calculate discreteness effects at early times in cosmological $N$-body simulations.

We present a detailed study of inflationary solutions in M theory with higher order quantum corrections. We first exhaust all exact and asymptotic solutions of exponential and power-law expansions in this theory with quartic curvature corrections, and then perform a linear perturbation analysis around fixed points for the exact solutions in order to see which solutions are more generic and give interesting cosmological models. We find an interesting solution in which the external space expands exponentially and the internal space is static both in the original and Einstein frames. Furthermore, we perform a numerical calculation around this solution and find numerical solutions which give enough $e$-foldings. We also briefly summarize similar solutions in type II superstrings.

We investigate the extent to which correlated distortions of the luminosity distance-redshift relation due to large-scale bulk flows limit the precision with which cosmological parameters can be measured. In particular, peculiar velocities of type 1a supernovae at low redshifts, $z<0.2$, may prevent a sufficient calibration of the Hubble diagram necessary to measure the dark energy equation of state to better than 10%, and diminish the resolution of the equation of state time-derivative projected for planned surveys. We consider similar distortions of the angular-diameter distance, as well as the Hubble constant. We show that the measurement of correlations in the large-scale bulk flow at low redshifts using these distance indicators may be possible with a cumulative signal-to-noise ratio of order 7 in a survey of 300 type 1a supernovae spread over 20 000 square degrees.

We discuss the behavior of strings propagating in spacetimes which allow future singularities of either a sudden future or a Big-Rip type. We show that in general the invariant string size remains finite at sudden future singularities while it grows to infinity at a Big-Rip. This claim is based on the discussion of both the tensile and null strings. In conclusion, strings may survive a sudden future singularity, but not a Big-Rip where they are infinitely stretched.

We calculate the spin dependent structure functions $g_1(x)$ and $g_2(x)$ of the proton and neutron. Our calculation uses the meson cloud model of nucleon structure, which has previously given a good description of the HERMES data on polarized sea quark distributions, and includes all the leading contributions to spin dependent effects in this model. We find good agreement between our calculations and the current experimental data for the structure functions. We include in our calculations kinematic terms, which mix transverse and longitudinal spin components, for hadrons of spin $1/2$, 1, and $3/2$, and which can give considerable contributions to the $g_2$ structure functions. We also consider the possible interference terms between baryons or mesons in different final states with the same quantum numbers, and show that most of these terms do not give leading contributions to the spin dependent structure functions.

In the light of the new prompt-photon data collected by PHENIX at RHIC and by D0 at the run II of the Tevatron, we revisit the world prompt-photon data, both inclusive and isolated, in hadronic collisions, and compare them with the NLO QCD calculations implemented in the Monte Carlo program JETPHOX.

We examine, as a correction to the central exclusive Higgs boson production in $pp$ collisions at the Large Hadron Collider, the rescattering of gluonic ladders off the proton. As usual, at the lowest order the hard part of this process can be described as a fusion of two hard gluonic ladders. We calculate corrections to this hard amplitude which are due to rescattering of these ladders. These corrections, which contain high mass diffractive excitations of the proton, have not yet been taken into account by the usual soft survival probabilities. We find that the correction due to the exchange of a single hard rescattering is negative, large, and infrared sensitive. As a first step towards a more reliable description we therefore replace the rescattering exchange by a unitarized amplitude using the Balitsky-Kovchegov equation which generates the saturation scale $Q_s(x)$. We also include a soft gap survival probability factor. We discuss the results and outline possible future strategies.

We show that the nonlinear chiral supermultiplet allows one to construct, over given two-dimensional bosonic mechanics, the family of two-dimensional $\mathcal{N}=4$ supersymmetric mechanics parametrized with the holomorphic function $\lambda (z)$. This observation contradicts the common understanding of the supersymmetrization procedure. We also show, that the constructed family includes, as a particular case, the $\mathcal{N}=4$ superextensions of two-dimensional mechanics with magnetic fields, which have factorizable Schrödinger equations.

We point out that the new interaction of spinning particles with the torsion tensor, discussed recently, is odd under charge conjugation and time reversal. This explains rather unexpected symmetry properties of the induced effective 4-fermion interaction.

We study the leading quantum effects in the recently introduced matrix big bang model. This amounts to a study of supersymmetric Yang-Mills theory compactified on the Milne orbifold. We find a one-loop potential that is attractive near the big bang. Surprisingly, the potential decays very rapidly at late times where it appears to be generated by $D$-brane effects. Usually, general covariance constrains the form of any effective action generated by renormalization group flow. However, the form of our one-loop potential seems to violate these constraints in a manner that suggests a connection between the cosmological singularity and long wavelength, late time physics.

We discuss the gravitational wave background produced by bouncing models based on a full quantum evolution of a universe filled with a perfect fluid. Using an ontological interpretation for the background wave function allows us to solve the mode equations for the tensorial perturbations, and we find the spectral index as a function of the fluid equation of state.

We investigate time dependent solutions (S-brane solutions) for product manifolds consisting of factor spaces where only one of them is non-Ricci-flat. Our model contains a minimally coupled free scalar field as a matter source. We discuss a possibility of generating late-time acceleration of the Universe. The analysis is performed in conformally related Brans-Dicke and Einstein frames. Dynamical behavior of our Universe is described by its scale factor. Since the scale factors of our Universe are described by different variables in both frames, they can have different dynamics. Indeed, we show that with our S-brane ansatz in the Brans-Dicke frame the stages of accelerating expansion exist for all types of the external space (flat, spherical, and hyperbolic). However, applying the same ansatz for the metric in the Einstein frame, we find that a model with flat external space and hyperbolic compactification of the internal space is the only one with the stage of the accelerating expansion. A scalar field can prevent this acceleration. It is shown that the case of hyperbolic external space in the Brans-Dicke frame is the only model which can satisfy experimental bounds for the fine-structure constant variations. We obtain a class of models where a pair of dynamical internal spaces have fixed total volume. This results in a fixed fine-structure constant. However, these models are unstable and external space is nonaccelerating.

We study the effects of magnetic fields on the evolution of differentially rotating neutron stars, which can be formed in stellar core collapse or binary neutron star coalescence. Magnetic braking and the magnetorotational instability (MRI) both act on differentially rotating stars to redistribute angular momentum. Simulations of these stars are carried out in axisymmetry using our recently developed codes which integrate the coupled Einstein-Maxwell-MHD equations. We consider stars with two different equations of state (EOS), a gamma-law EOS with $\Gamma =2$, and a more realistic hybrid EOS, and we evolve them adiabatically. Our simulations show that the fate of the star depends on its mass and spin. For initial data, we consider three categories of differentially rotating, equilibrium configurations, which we label normal, hypermassive and ultraspinning. Normal configurations have rest masses below the maximum achievable with uniform rotation, and angular momentum below the maximum for uniform rotation at the same rest mass. Hypermassive stars have rest masses exceeding the mass limit for uniform rotation. Ultraspinning stars are not hypermassive, but have angular momentum exceeding the maximum for uniform rotation at the same rest mass. We show that a normal star will evolve to a uniformly rotating equilibrium configuration. An ultraspinning star evolves to an equilibrium state consisting of a nearly uniformly rotating central core, surrounded by a differentially rotating torus with constant angular velocity along magnetic field lines, so that differential rotation ceases to wind the magnetic field. In addition, the final state is stable against the MRI, although it has differential rotation. For a hypermassive neutron star, the MHD-driven angular momentum transport leads to catastrophic collapse of the core. The resulting rotating black hole is surrounded by a hot, massive, magnetized torus undergoing quasistationary accretion, and a magnetic field collimated along the spin axis—a promising candidate for the central engine of a short gamma-ray burst.

Data from the Laser Interferometer Space Antenna (LISA) is expected to be dominated by frequency noise from its lasers. However, the noise from any one laser appears more than once in the data and there are combinations of the data that are insensitive to this noise. These combinations, called time delay interferometry (TDI) variables, have received careful study and point the way to how LISA data analysis may be performed. Here we approach the problem from the direction of statistical inference, and show that these variables are a direct consequence of a principal component analysis of the problem. We present a formal analysis for a simple LISA model and show that there are eigenvectors of the noise covariance matrix that do not depend on laser frequency noise. Importantly, these orthogonal basis vectors correspond to linear combinations of TDI variables. As a result we show that the likelihood function for source parameters using LISA data can be based on TDI combinations of the data without loss of information.

Electroweak production of single top quarks is still an unverified prediction of the standard model, potentially sensitive to new physics. Two of the single-top-quark production channels have significant charge asymmetries at the LHC, while the much larger background from $t\overline{t}$ is nearly charge symmetric. This can be used to reduce systematic uncertainties and make precision measurements of single-top-quark production.

We present a quenched lattice QCD calculation of the first few moments of the polarized and unpolarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing $a^{-1}\approx 1.3\mathrm{GeV}$, physical volume $V\approx (2.4\mathrm{fm}{)}^3$, and light quark masses down to about $1/4$ the strange quark mass ($m_{\pi }\approx 400\mathrm{MeV}$). Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of the flavor nonsinglet momentum fraction to the helicity distribution, $⟨x{⟩}_{u-d}/⟨x{⟩}_{\Delta u-{\Delta }_d}$, which is in very good agreement with experiment. We discuss the implications of this result. Next, we show that the chiral symmetry of domain wall fermions is useful in eliminating mixing of power divergent lower dimensional operators with twist-3 operators. Finally, we compute the isovector tensor charge at renormalization scale $\mu =2\mathrm{GeV}$ in the $\overline{MS}$ scheme, $⟨1{⟩}_{\delta u-\delta d}=1.192(30)$, where the error is the statistical error only.

In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin structure. So, we reformulate some simple electrostatic models in the presence of a spin-deformation contribution to the geometry of the motion, and we obtain an interesting correlation amongst the deformed area vector, the 3D noncommutative effects, and the usual spin vector $\overrightarrow{S}$ given in quantum mechanics framework. Remarkably we can observe that a spin-orbit coupling term comes to light on the spatial sector of a potential written in terms of noncommutative coordinates which indicates that bound states are particular cases in this procedure. Concerning confined or bounded particles in this noncommutative domain, we verify that the kinetic energy is modified by a deformation factor. Finally, we discuss perspectives.