We present numerical simulations of orbiting black holes for around 12 cycles, using a high order multipatch approach. Unlike some other approaches, the computational speed scales almost perfectly for thousands of processors. Multipatch methods are an alternative to adaptive mesh refinement, with benefits of simplicity and better scaling for improving the resolution in the wave zone. The results presented here pave the way for multipatch evolutions of black hole-neutron star and neutron star-neutron star binaries, where high resolution grids are needed to resolve details of the matter flow.

Supersymmetry implies that stable nontopological solitons, $Q$-balls, could form in the early universe and could make up all or part of dark matter. We show that the relic $Q$-balls passing through Earth can produce a detectable neutrino flux. The peculiar zenith angle dependence and a small annual modulation of this flux can be used as signatures of dark-matter $Q$-balls.

In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.

We present a Lagrangian for a massive, charged spin $3/2$ field in a constant external electromagnetic background, which correctly propagates only physical degrees of freedom inside the light cone. The Velo-Zwanziger acausality and other pathologies such as loss of hyperbolicity or the appearance of unphysical degrees of freedom are avoided by a judicious choice of nonminimal couplings. No additional fields or equations besides the spin $3/2$ ones are needed to solve the problem.

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti–)de Sitter black holes of Einstein gravity and IR limit of Hořava gravity are locally identical.

The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis in nonspherical geometry is very interesting as there may exist gravitational waves. We investigate self-similar vacuum solutions to the Einstein equation in the so-called whole-cylinder symmetry. We find that those solutions are reduced to part of the Minkowski spacetime with a regular or conically singular axis and with trivial or nontrivial topology if the homothetic vector is orthogonal to the cylinders of symmetry. These solutions are analogous to the Milne universe, but only in the direction parallel to the axis. Using these solutions, we discuss the nonuniqueness (and nonvanishing nature) of $C$ energy and the existence of a cylindrical trapping horizon in Minkowski spacetime. Then, as we generalize the analysis, we find a two-parameter family of self-similar vacuum solutions, where the homothetic vector is not orthogonal to the cylinders in general. The family includes the Minkowski, the Kasner, and the cylindrical Milne solutions. The obtained solutions describe the interior to the exploding (imploding) shell of gravitational waves or the collapse (explosion) of gravitational waves involving singularities from nonsingular initial data in general. Since recent numerical simulations strongly suggest that one of these solutions may describe the asymptotic behavior of gravitational waves from the collapse of a dust cylinder, this means that the self-similarity hypothesis is naturally generalized to cylindrical symmetry.

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einstein’s field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable with respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black hole or undergo a rapid expansion. Here, we consider charged generalization of the previous models by adding to the gravitational and ghost scalar field an electromagnetic one. We first derive the most general static, spherically symmetric wormholes in this theory and show that they give rise to a four-parameter family of solutions. This family can be naturally divided into subcritical, critical and supercritical solutions depending on the sign of the sum of the asymptotic masses. Then, we analyze the linear stability of these solutions. We prove that all subcritical and all critical solutions possess one exponentially in time growing mode. It follows that all subcritical and critical wormholes are linearly unstable. In the supercritical case we provide numerical evidence for the existence of a similar unstable mode.

The consequences of the constraints which stability of de Sitter solutions of $f(R)$ theories imposes on the Lagrangian’s parameters are investigated within the metric formalism. It is shown, in particular, that several common $f(R)$ Lagrangians do not actually admit matching of local solutions with background de Sitter spaces. Otherwise, asymptotic matching of local solutions of the corresponding models with maximally symmetric spaces of constant curvature is either unstable or anti–de Sitter space is the only stable asymptotic solution. Additional arguments are given in favor of a previous claim that a class of $f(R)$ models comprising both positive and negative powers of $R$ (two different mass scales) could be a nice scenario in which to address, in a united picture, both early-time inflation and late-time accelerated expansion of the Universe. The approach undertaken here is used, also, to check ghost freedom of a Dirac-Born-Infeld modification of general relativity previously studied in the literature.

After discussing the various possible interpretations of the $Y(4143)$ signal observed by the CDF collaboration in the $J/\psi \varphi$ mode, we tend to conclude that $Y(4143)$ is probably a $D_s^{*}{\overline{D}}_s^{*}$ molecular state with $J^{PC}=0^{++}$ or $2^{++}$ while $Y(3930)$ is its $D^{*}{\overline{D}}^{*}$ molecular partner as predicted in our previous work [X. Liu, Z. G. Luo, Y. R. Liu, and Shi-Lin Zhu, Eur. Phys. J. C 61, 411 (2009)]. Both the hidden-charm and open-charm two-body decays occur through the rescattering of the vector components within the molecular states while the three- and four-body open-charm decay modes are forbidden kinematically. Hence, their widths are narrow naturally. CDF, BABAR and Belle collaborations may have discovered heavy molecular states already. We urge experimentalists to measure their quantum numbers and explore their radiative decay modes in the future.

The quest to know the structure of matter has resulted in various theoretical speculations wherein additional colored fermions are postulated. Arising either as Kaluza-Klein excitations of ordinary quarks, or as excited states in scenarios wherein the quarks themselves are composites, or even in theories with extended gauge symmetry, the presence of such fermions ($q^{*}$) can potentially be manifested in $\gamma +\mathrm{\text{jet}}$ final states at the LHC. Using unitarized amplitudes and the CMS setup, we demonstrate that in the initial phase of LHC operation (with an integrated luminosity of $200{\mathrm{pb}}^{-1}$) one can discover such states for a mass up to 2.0 TeV. The discovery of a $q^{*}$ with a mass as large as $\sim 5\mathrm{TeV}$ can be achieved for an integrated luminosity of $\sim 140{\mathrm{fb}}^{-1}$. We also comment on the feasibility of mass determination.

We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory, the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at $O(a)$. As an application of our results we compute the pion decay constant to one loop in the two-flavor theory. Our result differs from previously published ones.

The scheme dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoretic models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising-type phase transition of the massive sine-Gordon model. For the latter case, the Maxwell construction represents a strong constraint on the RG flow, which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.

Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative ($l\ge 2$) second-order perturbations of a Schwarzschild black hole. In particular, we construct the second-order Zerilli and Regge-Wheeler equations under the presence of any two first-order modes, reconstruct the perturbed metric in terms of the master scalars, and compute the radiated energy at null infinity. The results of this paper enable systematic studies of generic second-order perturbations of the Schwarzschild spacetime, in particular, studies of mode-mode coupling and nonlinear effects in gravitational radiation, the second-order stability of the Schwarzschild spacetime, or the geometry of the black hole horizon.

Applying functional renormalization group methods, we describe two inequivalent ways of defining the renormalization group of matter-coupled four-dimensional gravity, in the approximation where only the conformal factor is dynamical and taking the trace anomaly explicitly into account. We make contact with earlier work and briefly discuss the presence or absence of fixed points, depending on the truncation of the action and other approximations.

We study the scale-dependent evolution of the growth function $\delta (a,k)$ of cosmological perturbations in dark energy models based on general relativity. This scale dependence is more prominent on cosmological scales of $100h^{-1}\mathrm{Mpc}$ or larger. We derive a new scale-dependent parametrization which generalizes the well-known Newtonian approximation result $f_0(a)\equiv \frac{d\ln {\delta }_0}{d\ln a}=\Omega (a{)}^{\gamma }$ ($\gamma =\frac{6}{11}$ for $\Lambda \mathrm{CDM}$) which is a good approximation on scales less than $50h^{-1}\mathrm{Mpc}$. Our generalized parametrization is of the form $f(a)=\frac{f_0(a)}{1+\xi (a,k)}$, where $\xi (a,k)=(3H_0^2{\Omega }_{0\mathrm{m}})/(a{k}^2)$. We demonstrate that this parametrization fits the exact result of a full general relativistic evaluation of the growth function up to horizon scales for both $\Lambda \mathrm{CDM}$ and dynamical dark energy. In contrast, the scale independent parametrization does not provide a good fit on scales beyond 5% of the horizon scale ($k\simeq 0.01h^{-1}\mathrm{Mpc}$).

The luminosity-redshift relation of cosmological standard candles provides information about the relative energy composition of our Universe. In particular, the observation of type Ia supernovae up to a redshift of $z\sim 2$ indicates a universe which is dominated today by dark matter and dark energy. The propagation distance of light from these sources is of the order of the Hubble radius and serves as a very sensitive probe of feeble inelastic photon interactions with background matter, radiation, or magnetic fields. In this paper we discuss the limits on minicharged particle models arising from a dimming effect in supernova surveys. We briefly speculate about a strong dimming effect as an alternative to dark energy.

The excesses of the cosmic positron fraction recently measured by PAMELA and the electron spectra by ATIC, PPB-BETS, Fermi, and H.E.S.S. indicate the existence of primary electron and positron sources. The possible explanations include dark matter annihilation, decay, and astrophysical origin, like pulsars. In this work we show that these three scenarios can all explain the experimental results of the cosmic $e^{\pm }$ excess. However, it may be difficult to discriminate these different scenarios by the local measurements of electrons and positrons. We propose possible discriminations among these scenarios through the synchrotron and inverse Compton radiation of the primary electrons/positrons from the region close to the Galactic center. Taking typical configurations, we find the three scenarios predict quite different spectra and skymaps of the synchrotron and inverse Compton radiation, though there are relatively large uncertainties. The most prominent differences come from the energy band ${10}^4\sim {10}^9\mathrm{MH}z$ for synchrotron emission and $\gtrsim 10\mathrm{GeV}$ for inverse Compton emission. It might be able to discriminate at least the annihilating dark matter scenario from the other two given the high precision synchrotron and diffuse $\gamma$-ray skymaps in the future.

We investigate the detection of exotic massive strongly interacting hadrons (uhecrons) in ultrahigh energy cosmic ray telescopes. The conclusion is that experiments such as the Pierre Auger Observatory have the potential to detect these particles. It is shown that uhecron showers have clear distinctive features when compared to proton and nuclear showers. The simulation of uhecron air showers, and its detection and reconstruction by fluorescence telescopes, is described. We determine basic cuts in observables that will separate uhecrons from the cosmic ray bulk, assuming this is composed by protons. If these are composed by a heavier nucleus, the separation will be much improved. We also discuss photon induced showers. The complementarity between uhecron detection in accelerator experiments is discussed.