We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under noncommutative Lorentz transformations. We then apply our idea to the case of actions obtained by expanding the star product and the fields taken in the enveloping algebra via the Seiberg-Witten maps and verify that these actions are invariant under these new noncommutative Lorentz transformations. We finally consider general coordinate transformations and show that the metric is undeformed.

We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein’s theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to nonprecessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between 1 and 2 orders of magnitude. We find that the bound on the coupling parameter ${\omega }_{\mathrm{BD}}$ of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte Carlo simulations of ${10}^4$ binaries, we show that inclusion of spin terms in massive black-hole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar-mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA’s low-frequency noise sensitivity can be extrapolated from ${10}^{-4}\mathrm{Hz}$ to as low as ${10}^{-5}\mathrm{Hz}$, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.

The dark energy model with the equation of state $p_d=-{\rho }_d-A{\rho }_d^{\alpha }$ is studied. The model comprises and provides realization of several types of singularities in different parameter regimes: the divergence of the dark energy density and pressure at finite time and finite value of the scale factor, the singularity of the “big rip” type and the sudden future singularity recently introduced by Barrow. For parameter choices which lead to a nonsingular expansion of the universe, various types of the asymptotic evolution are found. The entire time evolution of the universe is described both analytically and numerically. The advantages of this dark energy EOS as a parametrization of dark energy are discussed.

We apply the puncture approach to conformal thin-sandwich black-hole initial data. We solve numerically the conformal thin-sandwich puncture (CTSP) equations for a single black hole with nonzero linear momentum. We show that conformally-flat solutions for a boosted black hole have the same maximum gravitational radiation content as the corresponding Bowen-York solution in the conformal transverse-traceless decomposition. We find that the physical properties of these data are independent of the free slicing parameter.

The Tolman-Bondi and Vaidya solutions are two solutions to Einstein equations which describe dust particles and null fluid, respectively. We show that it is possible to match the two solutions in one single spacetime, the Tolman-Bondi-Vaidya spacetime. The new spacetime is divided by a null surface with Tolman-Bondi dust on one side and Vaidya fluid on the other side. The differentiability of the spacetime is discussed. By constructing a specific solution, we show that the metric across the null surface can be at least $C^1$ and the stress-energy tensor is continuous.

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such a factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.

We present fits to charmless strangeless hadronic $B$ decay data for mean branching ratios and $CP$-violating asymmetries using the QCD factorization model of Beneke et al. Apart from one $CP$-violating parameter, the model gives a very good representation of 26 measured data. We find the CKM angle $\alpha =(93.5\pm 8.4-1.3)°$ and to be quite stable to plausible “charming penguin” corrections.

We derive expressions for pion photoproduction amplitudes in the $1/N_c$ expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in $1/N_c$ compare favorably with available data, while the next-to-leading-order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at $O(1/N_c)$ or $O(1/N_c^2)$ is impressive.

We calculate one-loop R-parity violating corrections to the top quark decay into a bottom quark and a polarized W-gauge boson. The corrections are presented according to the total corrections, the longitudinal corrections and the transverse corrections, respectively. We compared our results with the $\mathcal{O}({\alpha }_s)$ QCD corrections, the $\mathcal{O}(\alpha )$ electroweak (EW) and finite width corrections, and also the supersymmetric (SUSY) corrections with R-parity conservation, respectively.

Isospin-breaking in $B\to \pi \pi$ caused by ${\pi }^0-\eta -{\eta }^{\prime }$ mixing is studied in a model-independent way using flavor SU(3). Measured branching ratios for $B^{+}\to {\pi }^{+}{\pi }^0,B^{+}\to {\pi }^{+}{\eta }^{{(}^{\prime })}$ and $B^0\to {\pi }^0{\eta }^{{(}^{\prime })}$ imply an uncertainty in $\alpha$ smaller than $1.4°$. We find a negligible effect of ${\pi }^0-\eta -{\eta }^{\prime }$ mixing on $\alpha$ in $B\to \rho \pi$. Characterizing the effect of ${\rho }^0-\omega$ mixing in $B\to \rho \rho$ and in $B\to \rho \pi$ by the two-pion invariant mass dependence, we point out a way of constraining this effect experimentally or eliminating it altogether. We show that a model-independent shift in $\alpha$ caused by electroweak penguin amplitudes in $B\to \pi \pi$, $B\to \rho \rho$ and $B\to \rho \pi$ is the same, $\Delta {\alpha }_{\mathrm{EWP}}=(1.5\pm 0.3)°$. Other sources of isospin-breaking in these processes are briefly discussed.

I construct predictive models of neutrino mass and mixing that have fewer parameters, both in the lepton sector and overall, than the default seesaw model. The predictions are ${\theta }_{13}=0$ and one massless neutrino, with the models having a $Z_4$ or $Z_2$ symmetry and just one extra degree of freedom: one real singlet Higgs field. It has been shown that models with an unbroken family symmetry, and with no Higgs fields other than the standard model Higgs doublet produce masses and mixing matrices that have been ruled out by experiment. Therefore, this article investigates the predictions of models with Abelian family symmetries that involve Higgs singlets, doublets and triplets, in the hope that they may produce the maximal and minimal mixing angles seen in the best-fit neutrino mixing matrix. I demonstrate that these models can only produce mixing angles that are zero, maximal or unconfined by the symmetry. The maximal mixing angles do not correspond to physical mixing, so an Abelian symmetry can, at best, ensure that ${\theta }_{13}=0$, while leaving the solar and atmospheric mixing angles as free parameters. To generate more features of the best-fit mixing matrix a model with a non-Abelian symmetry and a complicated Higgs sector would have to be used.

We study the electromagnetic properties of a system that consists of an electron background and a neutrino gas that may be moving or at rest, as a whole, relative to the background. The photon self-energy for this system is characterized by the usual transverse and longitudinal polarization functions, and two additional ones which are the focus of our calculations, that give rise to birefringence and anisotropic effects in the photon dispersion relations. Expressions for them are obtained, which depend on the neutrino number densities and involve momentum integrals over the electron distribution functions, and are valid for any value of the photon momentum and general conditions of the electron gas. Those expressions are evaluated explicitly for several special cases and approximations which are generally useful in astrophysical and cosmological settings. Besides studying the photon dispersion relations, we consider the macroscopic electrodynamic equations for this system, which involve the standard dielectric and permeability constants plus two additional ones related to the photon self-energy functions. As an illustration, the equations are used to discuss the evolution of a magnetic field perturbation in such a medium. This particular phenomena has also been considered in a recent work by Semikoz and Sokoloff as a mechanism for the generation of large-scale magnetic fields in the early Universe as a consequence of the neutrino-plasma interactions, and allows us to establish contact with a specific application in a well defined context, with a broader scope and from a very different point of view.

We find classical solutions of two dimensional noncritical string theory which give rise to geometries with spacelike boundaries, similar to spacetimes with cosmological event horizons. In the $c=1$ matrix model, these solutions have a representation as simple time-dependent configurations. We obtain the causal structure of the resulting spacetimes. Using the macroscopic loop transform, we probe the form of the tachyon condensate in the asymptotic regions.

We couple in superspace a dual vector multiplet $(C_{m_1\dots m_7},{\lambda }^{\alpha })$ to the dual version of $N=1$ supergravity $(e_m{}^a,\psi _m{}^{\alpha },M_{m_1\dots m_6},{\chi }_{\alpha },\Phi )$ in ten dimensions. The 7-form field $C$ has its 8-form field strength $H$ dual to the 2-form field strength $F$ of the conventional vector multiplet. To simplify the computation, we use so-called beta-function-favored superspace constraints for dual supergravity developed for $\beta$-function computations. As in a more conventional constraint set, the $H$-Bianchi identity must have the form $N\wedge F$, where $N$ is the 7-form field strength in dual supergravity. The potential anomaly for the dual vector multiplet can be cancelled for the particular gauge group $U(1{)}^{496}$ by the Green-Schwarz mechanism. As a by-product, we also give the globally supersymmetric Abelian Dirac-Born-Infeld interactions for the dual vector multiplet for the first time.

We present numerical results of three-dimensional simulations for the merger of binary neutron stars in full general relativity. Hybrid equations of state are adopted to mimic realistic nuclear equations of state. In this approach, we divide the equations of state into two parts as $P=P_{\mathrm{cold}}+P_{\mathrm{th}}$. $P_{\mathrm{cold}}$ is the cold part for which we assign a fitting formula for realistic equations of state of cold nuclear matter slightly modifying the formula developed by Haensel and Potekhin. We adopt the SLy and FPS equations of state for which the maximum allowed Arnowitt-Deser-Misner (ADM) mass of cold and spherical neutron stars is $\approx 2.04M_{\odot }$ and $1.80M_{\odot }$, respectively. $P_{\mathrm{th}}$ denotes the thermal part which is written as $P_{\mathrm{th}}=({\Gamma }_{\mathrm{th}}-1)\rho (\epsilon -{\epsilon }_{\mathrm{cold}})$, where $\rho$, $\epsilon$, ${\epsilon }_{\mathrm{cold}}$, and ${\Gamma }_{\mathrm{th}}$ are the baryon rest-mass density, total specific internal energy, specific internal energy of the cold part, and the adiabatic constant, respectively. Simulations are performed for binary neutron stars of the total ADM mass in the range between $2.4M_{\odot }$ and $2.8M_{\odot }$ with the rest-mass ratio $Q_M$ to be in the range $0.9\lesssim Q_M\le 1$. It is found that if the total ADM mass of the system is larger than a threshold $M_{\mathrm{thr}}$, a black hole is promptly formed in the merger irrespective of the mass ratios. In the other case, the outcome is a hypermassive neutron star of a large ellipticity, which results from the large adiabatic index of the realistic equations of state adopted. The value of $M_{\mathrm{thr}}$ depends on the equation of state: $M_{\mathrm{thr}}\sim 2.7M_{\odot }$ and $\sim 2.5M_{\odot }$ for the SLy and FPS equations of state, respectively. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of a large amplitude and of frequency between 3 and 4 kHz are emitted. The estimated emission time scale is $\lesssim 100\mathrm{ms}$, after which the hypermassive neutron star collapses to a black hole. Because of the long emission time, the effective amplitude may be large enough to be detected by advanced laser interferometric gravitational wave detectors if the distance to the source is smaller than $\sim 100\mathrm{Mpc}$. Thermal properties of the outcome formed after the merger are also analyzed to approximately estimate the neutrino emission energy.

By utilizing nonstandard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically-symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correction to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.

We discuss the effect of Kaluza-Klein (KK) modes of bulk metric perturbations on the second Randall-Sundrum (RS II) type brane cosmology, taking the possible backreaction in the bulk and on the brane into account. KK gravitons may be produced via quantum fluctuations during a de Sitter (dS) inflating phase of our brane universe. In an effective 4-dimensional theory in which one integrates out the extra-dimensional dependence in the action, KK gravitons are equivalent to massive gravitons on the brane with masses $m>3H/2$, where $H$ represents the expansion rate of a dS brane. Thus production of even a tiny amount of KK gravitons may eventually have a significant impact on the late-time brane cosmology. As a first step to quantify the effect of KK gravitons on the brane, we calculate the effective energy density and pressure for a single KK mode. Surprisingly, we find that a KK mode behaves as cosmic dust with a negative energy density on the brane. We note that the bulk energy density of a KK mode is positive definite and there occurs no singular phenomenon in the bulk.

We show that loitering at high redshifts ($z\gtrsim 6$) can easily arise in braneworld models of dark energy which, in addition to being spatially flat, also accelerate at late times. Loitering is characterized by the fact that the Hubble parameter dips in value over a narrow redshift range which we shall refer to as the “loitering epoch.” During loitering, density perturbations are expected to grow rapidly. In addition, since the expansion of the universe slows down, its age near loitering dramatically increases. An early epoch of loitering is expected to boost the formation of high-redshift gravitationally bound systems such as ${10}^9{M}_{\odot }$ black holes at $z\sim 6$ and lower-mass black holes and/or population III stars at $z>10$, whose existence could be problematic within the LCDM ($\mathrm{\text{lambda}}+\mathrm{\text{cold dark matter}}$) scenario. Loitering models also help to reduce the redshift of reionization from its currently (high) value of $z_{\mathrm{reion}}\simeq 17$ in LCDM cosmology, thus alleviating a significant source of tension between observations of the high-redshift universe and theoretical model building. Currently a loitering universe accelerates with an effective equation of state $w<-1$ thus mimicking phantom dark energy. Unlike phantom, however, the late-time expansion of the universe in our model is singularity free, and a universe that loitered in the past will approach a LCDM model asymptotically in the distant future.

We perform axisymmetric simulations for gravitational collapse of a massive iron core to a black hole in full general relativity. The iron cores are modeled by $\Gamma =4/3$ equilibrium polytrope for simplicity. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme with a parametric equation of state. The Cartoon method is adopted for solving the Einstein equations. Simulations are performed for a wide variety of initial conditions changing the mass ($\approx 2.0–3.0M_{\odot }$), the angular momentum, the rotational velocity profile of the core, and the parameters of the equations of state which are chosen so that the maximum mass of the cold spherical polytrope is $\approx 1.6M_{\odot }$. Then, the criterion for the prompt black hole formation is clarified in terms of the mass and the angular momentum for several rotational velocity profile of the core and equations of state. It is found that (i) with the increase of the thermal energy generated by shocks, the threshold mass for the prompt black hole formation is increased by 20–40%, (ii) the rotational centrifugal force increases the threshold mass by $\lesssim 25\%$, (iii) with the increase of the degree of differential rotation, the threshold mass is also increased, and (iv) the amplification factors shown in the results (i)–(iii) depend sensitively on the equation of state. We also find that the collapse dynamics and the structure of the shock formed at the bounce depend strongly on the stiffness of the adopted equation of state. In particular, as a new feature, a strong bipolar explosion is observed for the collapse of rapidly rotating iron cores with an equation of state which is stiff in subnuclear density and soft in supranuclear density. Gravitational waves are computed in terms of a quadrupole formula. It is also found that the waveform depends sensitively on the equations of state.

We study an effective four-dimensional theory with an action with two scalar fields minimally coupled to gravity, and with a matter action which couples to the two scalar fields via an overall field-dependent coefficient in the action. Such a theory could arise from a dimensional reduction of supergravity coupled to a gas of branes winding the compactified dimensions. We show the existence of solutions corresponding to power-law inflation. The graceful exit from inflation can be obtained by postulating the decay of the branes, as would occur if the branes are unstable in the vacuum and stabilized at high densities by plasma effects. This construction provides an avenue for connecting string gas cosmology and the late-time universe.