We obtain de Sitter (dS) and anti-de Sitter (AdS) generalized Reissner-Nordstrom–like black hole geometries in a curved ${\mathrm{D}}_3$-brane framework, underlying a noncommutative gauge theory on the brane world. The noncommutative scaling limit is explored to investigate a possible tunneling of an AdS vacuum in string theory to dS vacuum in its low energy gravity theory. The Hagedorn transition is invoked into its self-dual gauge theory to decouple the gauge nonlinearity from the dS geometry, which in turn is shown to describe a pure dS vacuum.

We develop a first-order approximation method for the influence of spin on the motion of extended spinning test masses in a gravitational field. This approach is illustrated for approximately circular equatorial motion in the exterior Kerr spacetime. In this case, the analytic results for the first-order approximation are compared to the numerical integration of the exact system and the limitations of the first-order results are pointed out. Furthermore, we employ our analytic results to illustrate the gravitomagnetic clock effect for spinning particles.

We study the hadron-quark phase transition in the interior of protoneutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the finite-temperature Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ the MIT bag model both with a constant and a density-dependent bag parameter. We calculate the structure of protostars with the equation of state comprising both phases and find maximum masses below 1.6 solar masses. Metastable heavy hybrid protostars are not found.

Models for dynamical breaking of supersymmetric grand unified theories are presented. The doublet-triplet splitting problem is absent since the Higgs-doublet superfields can be identified with the massless mesons of the strong gauge group whereas there are no massless states corresponding to the colored-Higgs fields. Various strong gauge groups $\mathrm{SU}(N_c)$, $\mathrm{Sp}(N_c)$, and $\mathrm{SO}(N_c)$ are examined. In a model with SO(9) strong gauge group, adding a $\mu$-term for the Higgs fields triggers to break supersymmetry in a metastable vacuum. The pattern of the supersymmetry breaking parameters is predicted to be of the gauge-mediation type with modifications in the Higgs sector.

We study effective lattice actions describing the Polyakov-loop dynamics originating from finite-temperature Yang-Mills theory. Starting with a strong-coupling expansion the effective action is obtained as a series of $\mathbb{Z}(3)$-invariant operators involving higher and higher powers of the Polyakov loop, each with its own coupling. Truncating to a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean-field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches concerning the phase structure of the theories. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic, and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents $\nu$ and $\gamma$ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state Potts model.

We analyze the change in position (the position shift) of the wave packet of a charged scalar particle due to radiation reaction in the $\hslash \to 0$ limit of quantum electrodynamics. In particular, we re-express the formula previously obtained for the position shift in terms of Green’s functions for the electromagnetic field, thus clarifying the relation between the quantum and classical derivations of the radiation-reaction force.

This work instigates a study of nonlocal field mappings within the Lorentz- and $CPT$-violating standard-model extension (SME). An example of such a mapping is constructed explicitly, and the conditions for the existence of its inverse are investigated. It is demonstrated that the associated field redefinition can remove $b^{\mu }$-type Lorentz violation from free SME fermions in certain situations. These results are employed to obtain explicit expressions for the corresponding Lorentz-breaking momentum-space eigenspinors and their orthogonality relations.

The possibility of testing spatial noncommutativity in the case of both position-position and momentum-momentum noncommuting via a Chern-Simons’ process is explored. A Chern-Simons process can be realized by an interaction of a charged particle in special crossed electric and magnetic fields, in which the Chern-Simons term leads to nontrivial dynamics in the limit of vanishing kinetic energy. Spatial noncommutativity leads to the spectrum of the orbital angular momentum possessing fractional values. Furthermore, in both limits of vanishing kinetic energy and subsequent vanishing magnetic field, the Chern-Simons term leads to this system having nontrivial dynamics again, and the dominant value of the lowest orbital angular momentum being $\hslash /4$, which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.

We derive the effective cosmological equations for a non-${\mathbb{Z}}_2$ symmetric codimension one brane embedded in an arbitrary $D$-dimensional bulk spacetime, generalizing the $D=5$, 6 cases much studied previously. As a particular case, this may be considered as a regularized codimension $(D-4)$ brane avoiding the problem of curvature divergence on the brane. We apply our results to the case of spherical symmetry around the brane and to partly compactified AdS-Schwarzschild bulks.

Strong numerical evidence is presented for the existence of a continuous family of time-periodic solutions with “weak” spatial localization of the spherically symmetric nonlinear Klein-Gordon equation in $3+1$ dimensions. These solutions are “weakly” localized in space in that they have slowly decaying oscillatory tails and can be interpreted as localized standing waves (quasibreathers). By a detailed analysis of long-lived metastable states (oscillons) formed during the time evolution, it is demonstrated that the oscillon states can be quantitatively described by the weakly localized quasibreathers. It is found that the quasibreathers and their oscillon counterparts exist for a whole continuum of frequencies.

The problem of mass generation is addressed by a Gaussian variational method for the minimal left-right symmetric model of electroweak interactions. Without any scalar bidoublet, the Gaussian effective potential is shown to have a minimum for a broken symmetry vacuum with a finite expectation value for both the scalar Higgs doublets. The symmetry is broken by the fermionic coupling that destabilizes the symmetric vacuum, yielding a self-consistent fermionic mass. In this framework a light Higgs is only compatible with the existence of a new high energy mass scale below 2 TeV.

We study the effects of a finite quark mass in the hedgehog configuration in the two phase chiral bag model. We discuss the chiral properties, such as the fractional baryon number and the chiral Casimir energy, by using the Debye expansion for the analytical calculation and the Strutinsky’s smearing method for the numerical computation. It is shown that the fractional baryon number carried by massive quarks in the vacuum is canceled by that in the meson sector. A finite term of the chiral Casimir energy is obtained with subtraction of the logarithmic divergence term.

We show a universal seesaw mechanism in the extra dimension theory. We take a left-right symmetric model in which extra three vectorlike fields exist in the 5D bulk. The universal seesaw formula is easily obtained as a replacement of the vectorlike mass in the 4D case $M_i$ to $2M_{*}\tan [\pi R{M}_i]$ ($M_{*}$: 5D Planck scale, $M_i$: vectorlike bulk mass, and $R$: compactification radius). The smallness of Dirac neutrino mass can be naturally explained in the 5D setup. We also show the Majorana neutrino case.

The decay width of the process $\eta \to {\pi }^0\gamma \gamma$ is calculated in the framework of the Nambu-Jona-Lasinio model. The momentum dependence of quark loops is taken into account. Three types of diagrams are considered: quark box, scalar ($a_0$) and vector $(\rho ,\omega )$ pole diagrams. The obtained estimations are in satisfactory agreement with recent experimental data.

We analyze homogeneous anisotropic cosmology driven by the dilaton and the self-interacting “massive” antisymmetric tensor field which are indispensable bosonic degrees with the graviton in the NS-NS sector of string theories with $D$-branes. We found the attractor solutions for this system, which show the overall features of general solutions, and confirmed it through numerical analysis. The dilaton possesses the potential due to the presence of the $D$-brane and the curvature of extra dimensions. In the presence of the nonvanishing antisymmetric tensor field, the homogeneous universe expands anisotropically while the $D$-brane term dominates. The isotropy is recovered as the dilaton rolls down and the curvature term dominates. With the stabilizing potential for the dilaton, the isotropy can also be recovered.

This paper is devoted to the computation of compact binaries composed of one black hole and one neutron star. The objects are assumed to be on exact circular orbits. Standard $3+1$ decomposition of Einstein equations is performed and the conformal flatness approximation is used. The obtained system of elliptic equations is solved by means of multidomain spectral methods. Results are compared with previous work both in the high mass ratio limit and for one neutron star with very low compactness parameter. The accuracy of the present code is shown to be greater than with previous codes. Moreover, for the first time, some sequences containing one neutron star of realistic compactness are presented and discussed.

The static cylindrically symmetric vacuum solutions with a cosmological constant in the framework of the Brans-Dicke theory are investigated. Some of these solutions admitting Lorentz boost invariance along the symmetry axis correspond to local, straight cosmic strings with a cosmological constant. Some physical properties of such solutions are studied. These strings apply attractive or repulsive forces on the test particles. A smooth matching is also performed with a recently introduced interior thick string solution with a cosmological constant.

We propose an evolutional scenario of the universe which starts from quantum states with conformal invariance, passing through the inflationary era, and then makes a transition to the conventional Einstein space-time. The space-time dynamics is derived from the renormalizable higher-derivative quantum gravity on the basis of a conformal gravity in four dimensions. Based on the linear perturbation theory in the inflationary background, we simulate evolutions of gravitational scalar, vector, and tensor modes, and evaluate the spectra at the transition point located at the beginning of the big bang. The obtained spectra cover the range of the primordial spectra for explaining the anisotropies in the homogeneous cosmic microwave background.

We confront the recent proposal of emerging brane inflation with $\mathrm{WMAP}3+\mathrm{SDSS}$, finding a scalar spectral index of $n_s={0.9659}_{-0.0052}^{+0.0049}$ in excellent agreement with observations. The proposal incorporates a preceding phase of isotropic, nonaccelerated expansion in all dimensions, providing suitable initial conditions for inflation. Additional observational constraints on the parameters of the model provide an estimate of the string scale. A graceful exit to inflation and stabilization of extra dimensions is achieved via a string gas. The resulting preheating phase shows some novel features due to a redshifting potential, comparable to effects due to the expansion of the universe itself. However, the model at hand suffers from either a potential overproduction of relics after inflation or insufficient stabilization at late times.

The coalescence of massive black holes generates gravitational waves (GWs) that will be measurable by space-based detectors such as LISA to large redshifts. The spins of a binary’s black holes have an important impact on its waveform. Specifically, geodetic and gravitomagnetic effects cause the spins to precess; this precession then modulates the waveform, adding periodic structure which encodes useful information about the binary’s members. Following pioneering work by Vecchio, we examine the impact upon GW measurements of including these precession-induced modulations in the waveform model. We find that the additional periodicity due to spin precession breaks degeneracies among certain parameters, greatly improving the accuracy with which they may be measured. In particular, mass measurements are improved tremendously, by one to several orders of magnitude. Localization of the source on the sky is also improved, though not as much—low redshift systems can be localized to an ellipse which is roughly $10-\mathrm{\text{a few}}\times 10\mathrm{arcminutes}$ in the long direction and a factor of 2 smaller in the short direction. Though not a drastic improvement relative to analyses which neglect spin precession, even modest gains in source localization will greatly facilitate searches for electromagnetic counterparts to GW events. Determination of distance to the source is likewise improved: We find that relative error in measured luminosity distance is commonly $\sim 0.1\%–0.4\%$ at $z\sim 1$. Finally, with the inclusion of precession, we find that the magnitude of the spins themselves can typically be determined for low redshift systems with an accuracy of about 0.1%–10%, depending on the spin value, allowing accurate surveys of mass and spin evolution over cosmic time.