A third post-Newtonian (3PN) equation of motion for an inspiraling binary consisting of two spherical compact stars with strong internal gravity is derived under the harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in the sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits the conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3PN equation of motion and an energy of the binary orbital motion in the case of a circular orbit (neglecting the 2.5PN radiation reaction effect) and in the center of mass frame. It is argued that the 3PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.

We suggest the possibility that in Arkani-Hamed–Dimopoulos–Dvali (ADD)-type brane-world scenarios the higher Kaluza-Klein (KK) excitations of the graviton may decay to lower ones owing to a breakdown of the conservation of extra dimensional “momenta” and study its implications for astrophysics and cosmology. We give an explicit realization of this idea with a bulk scalar field $\Phi ,$ whose nonzero KK modes acquire vacuum expectation values. This scenario helps to avoid constraints on large extra dimensions that come from gamma ray flux bounds in the direction of nearby supernovae as well as those coming from a diffuse cosmological gamma ray background. It also relaxes the very stringent limits on the reheat temperature of the Universe in ADD models.

The Weizsäcker-Williams method is a semiclassical approximation scheme used to analyze a wide variety of electromagnetic interactions. It can greatly simplify calculations that would otherwise be impractical or impossible to carry out using the standard route of the Feynman rules. The method is rederived here under the more general assumptions that the couplings are either electromagnetic, charged weak, or neutral weak, and that the fields are massive. All major formulas are found to reduce to those of the traditional method when appropriate limits are taken.

We show how the existence of nontrivial finite-energy time-dependent classical lumps is restricted by a generalized virial theorem. For simple model Lagrangians, bounds on energies follow.

We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville–von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analogue of the ${\phi }^4$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation, and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to $O\left({\lambda }^2\right).\mathrm{}$ These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected four-point functions in the hierarchy. The resulting coupled set of equations form part of an infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established, and the physical implications of the set of equations are discussed with particular emphasis on thermalization.

We examine the gauge generating nature of the translational subgroup of Wigner’s little group for the case of massless tensor gauge theories and show that the gauge transformations generated by the translational group are only a subset of the complete set of gauge transformations. We also show that, just as in the case of topologically massive gauge theories, translational groups act as generators of gauge transformations in gauge theories obtained by extending massive gauge noninvariant theories by a Stückelberg mechanism. The representations of the translational groups that generate gauge transformations in such Stückelberg extended theories can be obtained by the method of dimensional descent. We illustrate these results with the examples of Stückelberg extended first class versions of Proca, Einstein-Pauli-Fierz, and massive Kalb-Ramond theories in $3+1$ dimensions. A detailed analysis of the partial gauge generation in massive and massless second rank symmetric gauge theories is provided. The gauge transformations generated by the translational group in two-form gauge theories are shown to explicitly manifest the reducibility of gauge transformations in these theories.

We show that a flow (timelike congruence) in any type $B_1$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is written out explicitly for canonical representations of the spacetimes. With the flow determined, we explore an inverse approach to Einstein’s equations where a phenomenological fluid interpretation of a spacetime follows directly from the metric irrespective of the choice of coordinates. This approach is pursued for fluids with anisotropic pressure and shear viscosity. In certain degenerate cases this interpretation is shown to be generically not unique. The framework developed allows the study of exact solutions in any frame without transformations. We provide a number of examples, in various coordinates, including spacetimes with and without unique interpretations. The results and algorithmic procedure developed are implemented as a computer algebra program called GRSOURCE.

A detailed description of how black holes grow in full, nonlinear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. A change in the horizon area is related to these fluxes. A notion of angular momentum and energy is associated with cross sections of the horizon and balance equations, analogous to those obtained by Bondi and Sachs at null infinity, are derived. These in turn lead to generalizations of the first and second laws of black hole mechanics. The relation between dynamical horizons and their asymptotic states—the isolated horizons—is discussed briefly. The framework has potential applications to numerical, mathematical, astrophysical and quantum general relativity.

In this paper, we develop an iterative scheme to enable the explicit calculation of an arbitrary post-Newtonian order for a relativistic body that reduces to the Maclaurin spheroid in the appropriate limit. This scheme allows for an analysis of the structure of the solution in the vicinity of bifurcation points along the Maclaurin sequence. The post-Newtonian expansion is solved explicitly to the fourth order and its accuracy and convergence are studied by comparing it to highly accurate numerical results.

For a cosmological Randall-Sundrum braneworld with anisotropy, i.e., of Bianchi type, the modified Einstein equations on the brane include components of the five-dimensional Weyl tensor for which there are no evolution equations on the brane. If the bulk field equations are not solved, this Weyl term remains unknown, and many previous studies have simply prescribed it as ad hoc. We construct a family of Bianchi braneworlds with anisotropy by solving the five-dimensional field equations in the bulk. We analyze the cosmological dynamics on the brane, including the Weyl term, and shed light on the relation between anisotropy on the brane and the Weyl curvature in the bulk. In these models, it is not possible to achieve geometric anisotropy for a perfect fluid or scalar field—the junction conditions require anisotropic stress on the brane. But the solutions can isotropize and approach a Friedmann brane in an anti–de Sitter bulk.

We discuss a class of phantom $(p<\mathrm{}-\varrho )$ cosmological models. Except for the phantom we admit various forms of standard types of matter and discuss the problem of singularities for these cosmologies. The singularities are different from those of standard matter cosmology since they appear for infinite values of the scale factor. We also find an interesting relation between the phantom models and standard matter models which is like the duality symmetry of string cosmology.

We study the proton flux expected from sources of ultrahigh energy cosmic rays (UHECR) in the presence of regular extragalactic magnetic fields. It is assumed that a local source of ultrahigh energy protons and the magnetic field are all in a wall of matter concentration with dimensions characteristic of the supergalactic plane. For a single source, the observed proton flux and the local cosmic ray energy spectrum depend strongly on the strength of the field, the position of the observer, and the orientation of the field relative to the observer’s line of sight. Regular fields also affect protons emitted by sources outside the local magnetic fields structure. We discuss the possibility that such effects could contribute to an explanation of the excess of UHECR above $5\times {10}^{19}\mathrm{eV},$ and the possibility that sources of such particles may be missed if such magnetic fields are not taken into account.

Fermion masses and mixing matrices can be described in terms of spontaneously broken (global or gauge) flavor symmetries. We propose a little-Higgs-boson inspired scenario in which an $\mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ gauge flavor symmetry is spontaneously (and completely) broken by the vacuum of the dynamically induced potential for two scalar doublets (the flavons), which are pseudo Goldstone bosons remaining after the spontaneous breaking—at a scale between 10 and 100 TeV—of an approximate $\mathrm{SU}\left(6\right)\mathrm{}$ global symmetry. The vacuum expectation values of the flavons give rise to the texture in the fermion mass matrices. We discuss in detail the case of leptons. Light-neutrino masses arise by means of a seesawlike mechanism that takes place at the same scale at which the $\mathrm{SU}\left(6\right)\mathrm{}$ global symmetry is broken. We show that without any fine-tuning of the parameters the experimental values of the charged-lepton masses, the neutrino squared mass differences, and the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix are reproduced.

We present cross sections and differential distributions for QCD radiative corrections to the QCD processes $p\overrightarrow{p}W+2\mathrm{}$ jets and $p\overrightarrow{p}Z+2\mathrm{}$ jets at the CERN Large Hadron Collider (LHC). Calculations are performed with the Monte Carlo program MCFM. Cross section dependence on the renormalization and factorization scales is greatly reduced, except for the heavy-flavor case of $W^{\pm }b\overline{b},$ which has new features at next-to-leading order at the LHC. We also present cross sections for $W^{\pm }b\overline{b}$ and $Z+2\mathrm{}$ jets in kinematic configurations relevant for Higgs boson searches.

Using the monomer-dimer representation of strongly coupled $U\left(N\right)\mathrm{}$ lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in $2+1$ dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that the phase transition persists for all values of N, but occurs at different values of the critical temperature $T_c.$ Further, when ${T/T}_c$ is held fixed, the mean field analysis often used in the large N limit breaks down.

This paper investigates the possible cosmological implications of the presence of an antisymmetric tensor field $\theta$ related to a lack of commutativity of spacetime coordinates at the Planck era. For this purpose, $\theta$ is promoted to a dynamical variable, inspired by tensor formalism. By working to quadratic order in $\theta ,$ we study the field equations in a Bianchi type I Universe in two models: an antisymmetric tensor plus scalar field coupled to gravity, or a cosmological constant and a free massless antisymmetric tensor. In the first scenario, numerical integration shows that, in the very early Universe, the effects of the antisymmetric tensor can prevail on the scalar field, while at late times the former approaches zero and the latter drives the isotropization of the Universe. In the second model, an approximate solution is obtained of a nonlinear ordinary differential equation which shows how the mean Hubble parameter and the difference between longitudinal and orthogonal Hubble parameter evolve in the early Universe.

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world surface contains one lone self-intersection point which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.

Quantum weak energy inequalities (QWEIs) have been established for a variety of quantum field theories in both flat and curved spacetimes. Dirac fields are known (by a result of Fewster and Verch) to satisfy QWEIs under very general circumstances. However this result does not provide an explicit formula for the QWEI bound, so its magnitude has not previously been determined. In this paper we present a new and explicit QWEI bound for Dirac fields of mass $m>~0$ in four-dimensional Minkowski space. We follow the methods employed by Fewster and Eveson for the scalar field, modified to take account of anticommutation relations. A key ingredient is an identity for Fourier transforms established by Fewster and Verch. We also compare our QWEI with those previously obtained for scalar and spin-1 fields.

A detailed study is presented of the counterrotating model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure. A general constraint over the counterrotating tangential velocities, needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating perfect fluids, and expressions for the energy density and pressure of the counterrotating fluids are obtained. We show that, in general, it is not possible to take the two counterrotating fluids as circulating along geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of disks is studied that admits some CRMs with well defined counterrotating tangential velocities and stable against radial perturbations.

We review the circumstances under which test particles can be localized around a spacetime section ${\Sigma }_0$ smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, ${\Sigma }_0$ is said to be totally geodesic. Using three different methods, we derive a stability condition for trapped test particles in terms of intrinsic geometrical quantities on ${\Sigma }_0$ and M; namely, confined paths are stable against perturbations if the gravitational stress-energy density on M is larger than that on ${\Sigma }_0,$ as measured by an observed travelling along the unperturbed trajectory. We confirm our general result explicitly in two different cases: the warped-product metric ansatz for $\mathrm{}(n+1\mathrm{})\mathrm{}$-dimensional Einstein spaces, and a known solution of the 5-dimensional vacuum field equation embedding certain 4-dimensional cosmologies. We conclude by defining a confinement energy condition that can be used to classify geometries incorporating totally geodesic submanifolds, such as those found in thick braneworld and other 5-dimensional scenarios.