We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $\mathrm{\Psi }(t,r,\theta )=e^{im\theta }\mathrm{\Phi }(t,r)$, giving rise to an axisymmetric metric, in $2+1$ spacetime dimensions with cosmological constant $\mathrm{\Lambda }<0$, for $m=0$, 1, 2, for four one-parameter families of initial data. We look for the familiar scaling of black hole mass and maximal Ricci curvature as a power of $|p-p_{*}|$, where $p$ is the amplitude of our initial data and $p_{*}$ some threshold. We find evidence of Ricci scaling for all families, and tentative evidence of mass scaling for most families, but the case $m>0$ is very different from the case $m=0$ we have considered before: the thresholds for mass scaling and Ricci scaling are significantly different (for the same family); scaling stops well above the scale set by $\mathrm{\Lambda }$, and the exponents depend strongly on the family. Hence, in contrast to the $m=0$ case, and to many other self-gravitating systems, there is only weak evidence for the collapse threshold being controlled by a self-similar critical solution and no evidence for it being universal.

Even if the Higgs field does not affect the evolution of the background geometry, its massive inhomogeneities induce large-scale gauge fields whose energy density depends on the slow-roll parameters, on the effective scalar mass and, last but not least, on the dimensionless coupling to the spacetime curvature. Since the non-Abelian gauge modes are screened, the non-minimal coupling to gravity predominantly affects the evolution of the hypercharge and electromagnetic fields. While in the case of minimal coupling the obtained constraints are immaterial, as soon as the coupling increases beyond one-fourth, the produced fields become overcritical. We chart the whole parameter space of this qualitatively new set of bounds. Whenever the limits on the curvature coupling are enforced, the magnetic field may still be partially relevant for large-scale magnetogenesis and exceed ${10}^{-20}\mathrm{G}$ for the benchmark scale of the protogalactic collapse.

Stars on orbits with pericenters sufficiently close to the supermassive black hole at the center of their host galaxy can be ripped apart by tidal stresses. Some of the resulting stellar debris becomes more tightly bound to the hole and can potentially produce an observable flare called a tidal-disruption event (TDE). We provide a self-consistent, unified treatment of TDEs by nonspinning (Schwarzschild) black holes, investigating several effects of general relativity including changes to the boundary in phase space that defines the loss-cone orbits on which stars are tidally disrupted or captured. TDE rates decrease rapidly at large black hole masses due to direct stellar capture, but this effect is slightly countered by the widening of the loss cone due to the stronger tidal fields in general relativity. We provide a new mapping procedure that translates between Newtonian gravity and general relativity, allowing us to better compare predictions in both gravitational theories. Partial tidal disruptions in relativity will strip more material from the star and produce more tightly bound debris than in Newtonian gravity for a stellar orbit with the same angular momentum. However, for deep encounters leading to full disruption in both theories, the stronger tidal forces in relativity imply that the star is disrupted further from the black hole and that the debris is therefore less tightly bound, leading to a smaller peak fallback accretion rate. We also examine the capture of tidal debris by the horizon and the relativistic pericenter precession of tidal debris, finding that black holes of $10^6$ solar masses and above generate tidal debris precessing by 10° or more per orbit.

We have systematically investigated the magnetic moments and magnetic form factors of the decuplet baryons to the next-to-next-to-leading order in the framework of heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. We have also calculated the charge and magnetic dipole form factors of the decuplet baryons. Our results may be useful for the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.

The hadroquarkonium picture [S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008)] provides one possible interpretation for the pentaquark candidates with hidden charm, recently reported by the LHCb Collaboration, as well as for some of the charmoniumlike “$X$, $Y$, $Z$” states. In this picture, a heavy quarkonium core resides within a light hadron giving rise to four- or five-quark/antiquark bound states. We test this scenario in the heavy quark limit by investigating the modification of the potential between a static quark-antiquark pair induced by the presence of a hadron. Our lattice QCD simulations are performed on a Coordinated Lattice Simulations (CLS) ensemble with $N_f=2+1$ flavors of nonperturbatively improved Wilson quarks at a pion mass of about 223 MeV and a lattice spacing of about $a=0.0854\mathrm{fm}$. We study the static potential in the presence of a variety of light mesons as well as of octet and decuplet baryons. In all these cases, the resulting configurations are favored energetically. The associated binding energies between the quarkonium in the heavy quark limit and the light hadron are found to be smaller than a few MeV, similar in strength to deuterium binding. It needs to be seen if the small attraction survives in the infinite volume limit and supports bound states or resonances.

We consider the fragmentation of a parton into a jet with small radius $R$ in the large $z$ limit, where $z$ is the ratio of the jet energy to the mother parton energy. In this region of phase space, large logarithms of both $R$ and $1-z$ can appear, requiring resummation in order to have a well-defined perturbative expansion. Using the soft-collinear effective theory, we study the fragmentation function to a jet in this end-point region. We derive a factorization theorem for this object, separating collinear and collinear-soft modes. This allows for the resummation using renormalization group evolution of the logarithms $\ln R$ and $\ln (1-z)$ simultaneously. We show results valid to next-to-leading logarithmic order for the global Sudakov logarithms. We also discuss the possibility of nonglobal logarithms that should appear at two loops and give an estimate of their size.

Stimulated by the exciting progress in the observation of new bottomonium states, we study the bottomonium spectrum. To calculate the mass spectrum, we adopt a nonrelativistic screened potential model. The radial Schrödinger equation is solved with the three-point difference central method, where the spin-dependent potentials are dealt with nonperturbatively. With this treatment, the corrections of the spin-dependent potentials to the wave functions can be included successfully. Furthermore, we calculate the electromagnetic transitions of the $nS$ ($n\le 4$), $nP$ ($n\le 3$), and $nD$ ($n\le 2$) bottomonium states with a nonrelativistic electromagnetic transition operator widely applied to meson photoproduction reactions. Our predicted masses, hyperfine and fine splittings, electromagnetic transition widths, and branching ratios of the bottomonium states are in good agreement with the available experimental data. In particular, the EM transitions of $\mathrm{\Upsilon }(3S)\to {\chi }_{b1,2}(1P)\gamma$, which were not well understood in previous studies, can be reasonably explained by considering the corrections of the spin-dependent interactions to the wave functions. We also discuss the observations of the missing bottomonium states by using radiative transitions. Some important radiative decay chains involving the missing bottomonium states are suggested to be observed. We hope our study can provide some useful references to observe and measure the properties of bottomonium mesons in forthcoming experiments.

We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly virtual Compton scattering. For example, the polarizability ${\delta }_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability ${\gamma }_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.

Dyonic gaugings of four-dimensional supergravity typically exhibit a richer vacuum structure compared to their purely electric counterparts, but their higher-dimensional origin often remains more mysterious. We consider a class of dyonic gaugings with gauge groups of the type $(\mathrm{SO}(p,q)\times \mathrm{SO}(p^{\prime },q^{\prime }))⋉N$ with $N$ nilpotent. Using generalized Scherk-Schwarz reductions of exceptional field theory, we show how these four-dimensional gaugings may be consistently embedded in type II supergravity upon compactification around products of spheres and hyperboloids. As an application, we give the explicit uplift of the $\mathcal{N}=4$ ${\mathrm{AdS}}_4$ vacuum of the theory with gauge group $(\mathrm{SO}(6)\times \mathrm{SO}(1,1))⋉T^{12}$ into a supersymmetric ${\mathrm{AdS}}_4\times M_5\times S^1$ S-fold solution of IIB supergravity. The internal space $M_5$ is a squashed $S^5$ preserving an $\mathrm{SO}(4)\subset \mathrm{SO}(6)$ subset of its isometries.

We study chaos and turbulence on classical closed strings in nonintegrable string theory. The string motion is considered in the five-dimensional anti-de Sitter (AdS) soliton spacetime taken as the target space. We first revisit classical chaos using a cohomogeneity-1 string ansatz. We then turn to turbulent behaviors of the classical strings when the spatial dependence of the string world sheet is included. Sensitivity to initial conditions in chaotic systems suggests that the string under chaos tends to stretch in the AdS soliton spacetime in a Lyapunov time scale. In this process, the orbital angular momentum transfers to internal spin due to the turbulence on the string. It follows that the string stays around the tip of the AdS soliton with a jumbled profile. We evaluate the spectra of conserved quantities and discuss their universal power-law scalings in the turbulent behaviors.

We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that $j^3$, the $z$-component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of $j^3$ under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.

Our goal in this work is to present the variational method of fictitious parameters and its connection with the Bechi-Rouet-Stora-Tyutin (BRST) symmetry. First, we implement the method in QED at zero temperature and then we extend the analysis to generalized QED at finite temperature. As we see the core of the study is the general statement in gauge theories at finite temperature, assigned by Tyutin work, that the physical degrees of freedom do not depend on the gauge choices, covariant or not, due to BRST symmetry.

The singularity theorem by Hawking and Penrose qualifies Schwarzschild black holes as geodesic incomplete space-times. Albeit this is a mathematically rigorous statement, it requires an operational framework that allows us to probe the spacelike singularity via a measurement process. Any such framework necessarily has to be based on quantum theory. As a consequence, the notion of classical completeness needs to be adapted to situations where the only adequate description is in terms of quantum fields in dynamical space-times. It is shown that Schwarzschild black holes turn out to be complete when probed by self-interacting quantum fields in the ground state and in excited states. The measure for populating quantum fields on hypersurfaces in the vicinity of the black-hole singularity goes to zero towards the singularity. This statement is robust under non-Gaussian deformations of and excitations relative to the ground state. The physical relevance of different completeness concepts for black holes is discussed.

Time-dependent analytic solutions of the Einstein-Skyrme system—gravitating Skyrmions—with topological charge are analyzed in detail. In particular, the question of whether these Skyrmions reach a spherically symmetric configuration for $t\to +\infty$ is discussed. It is shown that there is a static, spherically symmetric solution described by the Ermakov-Pinney system, which is fully integrable by algebraic methods. For $\mathrm{\Lambda }>0$, this spherically symmetric solution is found to be in a “neutral equilibrium” under small deformations, in the sense that under a small squashing it would neither blow up nor disappear after a long time, but it would remain finite forever (plastic deformation). Thus, in a sense, the coupling with Einstein gravity spontaneously breaks the spherical symmetry of the solution. However, in spite of the lack of isotropy, for $t\to \infty$ (and $\mathrm{\Lambda }>0$), the spacetime is locally flat and the anisotropy of the Skyrmion only reflects the squashing of spacetime.

We present an elementary argument that one can shield linearized gravitational fields using linearized gravitational fields. This is done by using third-order potentials for the metric, which avoids the need to solve singular equations in shielding or gluing constructions for the linearized metric.

A fourth-order theory of gravity is considered which in terms of dynamics has the same degrees of freedom and number of constraints as those of scalar-tensor theories. In addition, it admits a canonical pointlike Lagrangian description. We study the critical points of the theory, and we show that it can describe the matter epoch of the Universe and that two accelerated phases can be recovered, one of which describes a de Sitter universe. Finally, for some models exact solutions are presented.

We reanalyze the nonlocal gravity model of Deser and Woodard, which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-Lambda-cold-dark-matter ($\mathrm{\Lambda }\mathrm{CDM}$) models can be substantially lower than when its background is fixed by $\mathrm{\Lambda }\mathrm{CDM}$. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hint towards a fact that the choice of the background expansion can play a crucial role in how this nonlocal gravity model can fit the growth history data. While the growth data might show better consistency to general relativity (GR) models (among the background models we studied so far), it seems the nonlocal gravity model studied in this work is able to show comparable consistency to the growth data as well. Showing this consistency can be considered as a significant result since this model can stand as a distinguishable alternative to the standard model of cosmology.

$R$-modes of neutron stars could be a source of gravitational waves for ground based detectors. If the precise $r$-mode frequency $\sigma$ in an inertial frame is known, guided gravitational wave searches with enhanced detectability are possible. Because of its physical importance, many authors have calculated the $r$-mode frequency. For the dominant mode, the associated gravitational wave frequency is $4/3$ times the angular velocity of the star $\mathrm{\Omega }$, subject to various corrections of which relativistic and rotational corrections are the most important. This has led several authors to investigate the dependence of the $r$-mode frequency on factors such as the relativistic compactness parameter $M/R$ and the angular velocity of stars with different equations of state. The results found so far, however, are almost independent of the equation of state. Here, we investigate the effect of rapid rotation and differential rotation on $\sigma$. We work with a series of rotating neutron stars with polytropic equations of state, and we perform the time evolution of the linear perturbation equations in the relativistic Cowling approximation with a finite-difference code. We find that rotational effects in the $r$-mode frequency can be larger than relativistic effects for rapidly spinning stars with low compactness, reducing the observed frequency. Differential rotation also acts to decrease $\sigma$, but its effect increases with the compactness. The results presented here are relevant to the design of gravitational-wave and electromagnetic $r$-mode searches.