In backgrounds with compact dimensions there may exist several phases of black objects including a black hole and a black string. The phase transition between them raises questions and touches on fundamental issues such as topology change, uniqueness, and cosmic censorship. No analytic solution is known for the black hole, and moreover one can expect approximate solutions only for very small black holes, while phase transition physics happens when the black hole is large. Hence we turn to numerical solutions. Here some theoretical background to the numerical analysis is given, while the results will appear in a subsequent paper. The goals for a numerical analysis are set. The scalar charge and tension along the compact dimension are defined and used as improved order parameters which put both the black hole and the black string at finite values on the phase diagram. The predictions for small black holes are presented. The differential and the integrated forms of the first law are derived, and the latter (Smarr’s formula) can be used to estimate the “overall numerical error.” Field asymptotics and expressions for physical quantities in terms of the numerical values are supplied. The techniques include the “method of equivalent charges,” free energy, dimensional reduction, and analytic perturbation for small black holes.

The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor $R_{{}_{\vee }^{\mu \nu }},$ consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with $R_{{}_{\vee }^{\mu \nu }}=0\mathrm{}$ the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al., to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field.

We propose a self-consistent and dynamical scenario which gives rise to well-defined initial conditions for five-dimensional brane-world cosmologies with radion stabilization. At high energies, the five-dimensional effective theory is assumed to have a scale invariance so that it admits an expanding scaling solution as a future attractor. The system automatically approaches the scaling solution and, hence, the initial condition for the subsequent low-energy brane cosmology is set by the scaling solution. At low energies, the scale invariance is broken and a radion stabilization mechanism drives the dynamics of the brane-world system. We present an exact, analytic scaling solution for a class of scale-invariant effective theories of five-dimensional brane-world models which includes the five-dimensional reduction of the Horava-Witten theory, and provide convincing evidence that the scaling solution is a future attractor.

We consider stationary rotating black holes in SU(2) Einstein-Yang-Mills theory, coupled to a dilaton. The black holes possess nontrivial non-Abelian electric and magnetic fields outside their regular event horizon. While generic solutions carry no non-Abelian magnetic charge, but non-Abelian electric charge, the presence of the dilaton field allows also for rotating solutions with no non-Abelian charge at all. As a consequence, these special solutions do not exhibit the generic asymptotic noninteger power falloff of the non-Abelian gauge field functions. The rotating black hole solutions form sequences, characterized by the winding number n and the node number k of their gauge field functions, tending to embedded Abelian black holes. The stationary non-Abelian black hole solutions satisfy a mass formula, similar to the Smarr formula, where the dilaton charge enters instead of the magnetic charge. Introducing a topological charge, we conjecture that black hole solutions in SU(2) Einstein-Yang-Mills-dilaton theory are uniquely characterized by their mass, their angular momentum, their dilaton charge, their non-Abelian electric charge, and their topological charge.

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, and it is shown that, given the distribution of density and pressure profiles at the initial surface from which the collapse evolves, there is freedom in choosing the rest of the free functions and dynamical collapse evolutions from these initial data, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. Our results give some physical insight into these collapse outcomes as to how these phases come about.

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate “astrophysically relevant” initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.

The influence of the shape of the scalar field potential on the outcome of vacuum decay in a de Sitter universe is studied. The sufficient condition for vacuum decay via bubble formation, described by the Coleman–de Luccia instanton, is examined and a necessary condition is found. Both conditions require the curvature of the potential to be greater than $4\times (\mathrm{Hubble}\mathrm{}\mathrm{constant}{)}^2,$ but while the sufficient condition states that this inequality is to be valid at the top of the barrier, the necessary condition requires that it holds at least somewhere within the barrier. The conditions leave a “gray zone” in the parameter space which, however, seems to be forbidden for a quartic potential.

VAMP (variable-mass particle) scenarios, in which the mass of the cold dark matter particles is a function of the scalar field responsible for the present acceleration of the Universe, have been proposed as a solution to the cosmic coincidence problem, since in the attractor regime both dark energy and dark matter scale in the same way. We find that only a narrow region in parameter space leads to models with viable values for the Hubble constant and dark energy density today. In the allowed region, the dark energy density starts to dominate around the present epoch and consequently such models cannot solve the coincidence problem. We show that the age of the Universe in this scenario is considerably higher than the age for noncoupled dark energy models, and conclude that more precise independent measurements of the age of the Universe would be useful in distinguishing between coupled and noncoupled dark energy models.

We investigate anomalies reported in the cosmic microwave background maps from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite on very large angular scales and discuss possible interpretations. Three independent anomalies involve the quadrupole and octopole: (1) The cosmic quadrupole on its own is anomalous at the 1-in-20 level by being low (the cut-sky quadrupole measured by the WMAP team is more strikingly low, apparently due to a coincidence in the orientation of our Galaxy of no cosmological significance); (2) the cosmic octopole on its own is anomalous at the 1-in-20 level by being very planar; (3) the alignment between the quadrupole and octopole is anomalous at the 1-in-66 level. Although the a priori chance of all three occurring is 1 in 24000, the multitude of alternative anomalies one could have looked for dilutes the significance of such a posteriori statistics. The simplest small universe model where the universe has toroidal topology with one small dimension of order one-half the horizon scale, in the direction toward Virgo, could explain the three items above. However, we rule this model out using two topological tests: the S statistic and the matched circle test.

Gravitational lensing introduces the possibility of multiple (macroscopic) paths from an astrophysical neutrino source to a detector. Such a multiplicity of paths can allow for quantum mechanical interference to take place that is qualitatively different from neutrino oscillations in flat space. After an illustrative example clarifying some underappreciated subtleties of the phase calculation, we derive the form of the quantum mechanical phase for a neutrino mass eigenstate propagating nonradially through a Schwarzschild metric. We subsequently determine the form of the interference pattern seen at a detector. We show that the neutrino signal from a supernova could exhibit the interference effects we discuss were it lensed by an object in a suitable mass range. We finally conclude, however, that—given current neutrino detector technology—the probability of such lensing occurring for a (neutrino-detectable) supernova is tiny in the immediate future.

We present a comparison between three approaches to test the non-Gaussianity of cosmic microwave background data. The Minkowski functionals, the empirical process method, and the skewness of wavelet coefficients are applied to maps generated from nonstandard inflationary models and to Gaussian maps with point sources included. We discuss the different power of the pixel, harmonic, and wavelet space methods on these simulated almost full-sky data (with Planck-like noise). We also suggest a new procedure consisting of a combination of statistics in pixel, harmonic, and wavelet space.

In this Brief Report, we clarify a point concerning the power divergence in lattice calculations of $\Delta I=1/2\mathrm{}\overrightarrow{K}\pi \pi$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at $M_K{=M}_{\pi }$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order chiral perturbation theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.

A low-energy supersymmetry scenario with a light gluino of mass 12–16 GeV and light sbottom $\left(b_1\right)$ of mass 2–6 GeV has been used to explain the apparent overproduction of b quarks at the fermilab Tevatron. In this scenario the other mass eigenstate of the sbottom, i.e., $b_2,$ is favored to be lighter than 180 GeV due to constraints from electroweak precision data. We survey its decay modes in this scenario and show that decay into a b quark and gluino should be dominant. Associated sbottom production at CERN LEP via $e^{+}{e}^{-}\to Z^{*}\to b_1{b}_2^{*}+b_1^{*}{b}_2$ is studied and we show that it is naturally a three-jet process with a small cross section, increasingly obscured by a large standard model background for heavier $b_2.$ However we find that direct observation of a $b_2$ at the $5\sigma$ level is possible if it is lighter than 110–129 GeV, depending on the sbottom mixing angle $|\cos {\theta }_b|=0.30\mathrm{}–\mathrm{0.45.}$ We also show that $b_2$-pair production can be mistaken for production of neutral minimal supersymmetric standard model Higgs bosons in the channel $e^{+}{e}^{-}\to h^0{A}^0\to b\overline{b}b\overline{b}.$ Using searches for the latter we place a lower mass limit of 90 GeV on $b_2.$

Recent data for the ratio ${R\left(Q\right)=QF}_2{(Q}^2{)/F}_1{(Q}^2)$ surprised the community by disobeying expectations held for 50 years. It was widely thought that $R\left(Q\right)\mathrm{}\sim 1/Q$ was also a rigorous prediction of PQCD. We examine the status of perturbative QCD predictions for helicity-flip form factors. Contrary to common belief, we find there is no rule of hadron helicity conservation for form factors. Numerical calculations support asymptotic analysis and extend it to the regime of laboratory momentum transfer $Q^2.$ Quark orbital angular momentum, an important feature of the helicity flip processes, may play a role in all form factors at large $Q^2,$ depending on the quark wave functions.

Starting with the hypothesis that quark and lepton mixings are identical at or near the grand unified theory scale, we show that the large solar and atmospheric neutrino mixing angles together with the small reactor angle $U_{e3\mathrm{}}$ can be understood purely as a result of renormalization group evolution provided the three neutrinos are quasidegenerate and have the same CP parity. The mechanism is found to work if the common Majorana mass for the neutrinos is larger than 0.1 eV, which falls right in the range reported recently and also in the range which will be probed in planned experiments.

We use a neural-network technique to search for standard model single-top-quark production in the $106{\mathrm{pb}}^{-1}$ dataset accumulated by the Collider Detector at Fermilab detector during the 1992–1995 collider run (“run I”). Using a sample of 64 $W+1,$ 2, 3 jets events, we set a 95% confidence level upper limit of 24 pb on the W-gluon and $W^{*}$ combined single-top cross section.

Several recent experiments have reported evidence for a narrow baryon resonance with positive strangeness $\left({\Theta }^{+}\right)$ at a mass of $1.54\mathrm{GeV}{/c}^2.$ Baryons with $S=+1\mathrm{}$ cannot be conventional qqq states and the reports have thus generated much theoretical speculation about the nature of possible $S=+1\mathrm{}$ baryons, including a 5-quark, or pentaquark, interpretation. We show that narrow enhancements in the $K^{+}n$ effective mass spectrum can be generated as kinematic reflections resulting from the decay of mesons, such as the $f_2\mathrm{}\left(1275\right),$ the $a_2\mathrm{}\left(1320\right)\mathrm{}$ and the ${\rho }_3\mathrm{}\left(1690\right).$

We study gravity duals of large N nonsupersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a nonconstant dilaton and $S^5$ radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the $\overline{\Psi }\Psi$ condensate and meson spectrum associated with these backgrounds. In the AdS–black-hole background, a quark-bilinear condensate develops only at a nonzero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

We correct an unfortunate error in an earlier work of the author, and show that in the center-vortex picture of QCD [gauge group $\mathrm{SU}\left(3\right)\mathrm{}]$ the asymptotic quenched baryonic area law is the so-called Y law, described by a minimal area with three surfaces spanning the three quark world lines and meeting at a central Steiner line joining the two common meeting points of the world lines. (The earlier claim was that this area law was a so-called $\Delta$ law, involving three extremal areas spanning the three pairs of quark world lines.) By asymptotic we mean the Y law holds at asymptotically large quark separations from each other; at separations of the order of the gauge-theory scale length, there may be Δ-like contributions. We give a preliminary discussion of the extension of these results to $\mathrm{SU}\left(N\right),N>\mathrm{}3.\mathrm{}$ These results are based on the (correct) baryonic Stokes’ theorem given in the earlier work claiming a Δ law. The Y-form area law for $\mathrm{SU}\left(3\right)\mathrm{}$ is in agreement with the most recent lattice calculations.

We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild–de Sitter spacetimes. Our results show that for low-order quasinormal modes the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is quite a good approximation for the quasinormal frequencies as long as the model parameter $r_1{\kappa }_1$ is small enough, where $r_1$ and ${\kappa }_1$ are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which correspond quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of $r_1{\kappa }_1.$ We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordström black hole. The amplitude of oscillating $\mathrm{Re}\left(\mathrm{\omega }\mathrm{}\right)$ as a function of $\mathrm{Im}\left(\omega \right)$ approaches a nonzero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where $\omega$ denotes the quasinormal frequency. This means that for gravitational perturbations the real part of the quasinormal modes of the nearly extremal Schwarzschild–de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of the frequency seems to go to zero in the limit.