An infinite family of new exact solutions of the vacuum Einstein equations is presented. The solutions are static and axially symmetric and correspond to an infinite family of thin dust disks with a central inner edge. The metric functions of all the solutions can be explicitly computed, and can be expressed in a simple manner in terms of oblate spheroidal coordinates. The energy density of all the disks of the family is positive everywhere and well behaved, so that the corresponding energy-momentum tensor is in full agreement with all the energy conditions. Moreover, although the total mass of the disks is infinite, the solutions are asymptotically flat and the Riemann tensor is regular everywhere, as it is shown by computing the curvature scalars. Now, besides its importance as a new family of exact solutions of the vacuum Einstein equations, the main importance of this family of solutions is that it can be easily superposed with the Schwarzschild solution in order to describe thin disks surrounding a central black hole. Accordingly, a detailed analysis of this superposition will be presented in a subsequent paper.

We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple models for the motion of a massive point particle in a fixed causal set background. If the causal set is faithfully embeddable in Minkoswki spacetime, the models give rise to particle motion in the continuum spacetime. At large scales, the microscopic swerves induced by the underlying atomicity manifest themselves as a Lorentz invariant diffusion in energy-momentum governed by a single phenomenological parameter, and we derive in full the corresponding diffusion equation. Inspired by the simplicity of the result, we then derive the most general Lorentz invariant diffusion equation for a massless particle, which turns out to contain two phenomenological parameters describing, respectively, diffusion and drift in the particle’s energy. The particles do not leave the light cone however: their worldlines continue to be null geodesics. Finally, we deduce bounds on the drift and diffusion constants for photons from the blackbody nature of the spectrum of the cosmic microwave background radiation.

Black branes are studied in Einstein-Gauss-Bonnet gravity. Evaporation drives black branes toward one of two singularities depending on the sign of $\alpha$, the Gauss-Bonnet coupling. For positive $\alpha$ and sufficiently large ratio $\sqrt{\alpha }/L$, where $L/2\pi$ is the radius of compactification, black branes avoid the Gregory-Laflamme (GL) instability before reaching a critical state. No black branes with the radius of horizon smaller than the critical value can exist. Approaching the critical state branes have a nonzero Hawking temperature. For negative $\alpha$ all black branes encounter the GL instability. No black branes may exist outside of the interval of the critical values $0\le \beta <3$, where $\beta =1-8\alpha /r_h^2$ and $r_h$ is the radius of horizon of the black brane. The first order phase transition line of GL transitions ends in a second order phase transition point at $\beta =0$.

We calculate the direct dark matter detection spin-independent and proton spin-dependent cross sections for a semirealistic intersecting $D6$-brane model. The cross sections are compared to the latest constraints of the current dark matter direct detection experiments, as well as the projected results of future dark matter experiments. The allowed parameter space of the intersecting $D6$-brane model is shown with all current experimental constraints, including those regions satisfying the WMAP and supercritical string cosmology limits on the dark matter density in the Universe. Additionally, we compute the indirect detection gamma-ray flux resulting from neutralino annihilation for the $D6$-brane model and compare the flux to the projected sensitivity of the Fermi Gamma-ray Space Telescope. Finally, we compute the direct and indirect detection cross sections as well as the gamma-ray flux resulting from weakly interacting massive particle annihilations for the one-parameter model for comparison, where the one-parameter model is a highly constrained subset of the minimal supergravity parameter space such that the soft-supersymmetry-breaking terms are functions of the common gaugino mass, which is common to many string compactifications.

The electroweak phase transition and the sphaleron decoupling condition in the minimal supersymmetric standard model are revisited taking the latest experimental data into account. The light Higgs boson scenario and the ordinary decoupling limit, which are classified by the relative size between the $CP$-odd Higgs boson mass and $Z$ boson mass, are considered within the context of electroweak baryogenesis. We investigate $v/T$ at not only the critical temperature at which the effective potential has two degenerate minima but also the nucleation temperature of the critical bubbles, where $v$ is a vacuum expectation value of the Higgs boson and $T$ denotes a temperature. It is found that $v/T$ at the nucleation temperature can be enhanced by about 10% compared to that at the critical temperature. We also evaluate the sphaleron decoupling condition including the zero mode factors of the fluctuations around sphaleron. It is observed that the sphaleron decoupling condition at the nucleation temperature is given by $v/T\gtrsim 1.38$ for the typical parameter sets. In any phenomenologically allowed region, $v/T$ at both the critical and nucleation temperatures cannot be large enough to satisfy such a sphaleron decoupling condition.

Since the structure of space-time at very short distances is believed to get modified possibly due to noncommutativity effects and as the Dirac quantization condition, $\mu e=\frac{N}{2}\hslash c$, probes the magnetic field point singularity, a natural question arises whether the same condition will still survive. We show that the Dirac quantization condition on a noncommutative space in a model of dynamical noncommutative quantum mechanics remains the same as in the commutative case to first order in the noncommutativity parameter $\theta$, leading to the conjecture that the condition will not alter in higher orders.

A detailed nonlinear analysis of the internal structure of spherical, charged black holes that are accreting scalar matter is performed in the framework of the Brans-Dicke theory of gravity. We choose the lowest value of the Brans-Dicke parameter that is compatible with observational constraints. First, the homogeneous approximation is used. It indicates that mass inflation occurs and that the variations of the Brans-Dicke scalar inside the black hole, which could in principle be large in the absence of mass inflation, become small when mass inflation does occur. Then, a full nonlinear numerical study of the black hole interior perturbed by a self-gravitating massless uncharged scalar field is performed. We use an algorithm with adaptive mesh refinement capabilities. In this way, the changes in the internal structure of the black hole caused by mass inflation are determined, as well as the induced variations of the Brans-Dicke scalar, confirming, qualitatively, the indications given by the homogeneous approximation.

We investigate the scalar Green function for spherically symmetric spacetimes expressed as a coordinate series expansion in the separation of the points. We calculate the series expansion of the function $V(x,x^{\prime })$ appearing in the Hadamard parametrix of the scalar Green function to very high order. This expansion is then used to investigate the convergence properties of the series and to estimate its radius of convergence. Using the method of Padé approximants, we show that the series can be extended beyond its radius of convergence to within a short distance of the normal neighborhood boundary.

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of “matched expansions” to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the “quasilocal” and “distant past” regimes, and which may be matched together within the normal neighborhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime ($d{S}_2\times {\mathbb{S}}^2$), in which scalar-field perturbations are governed by a radial equation with a Pöschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever $x$ and $x^{\prime }$ are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence $\delta (\sigma )$, $1/\pi \sigma$, $-\delta (\sigma )$, $-1/\pi \sigma$, etc., where $\sigma$ is Synge’s world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on a static particle on the Nariai spacetime, and validate against an alternative method, obtaining agreement to six decimal places. We conclude with a discussion of the implications for wave propagation and self-force calculations. On black hole spacetimes, any expansion of the Green function in quasinormal modes must be augmented by a branch-cut integral. Nevertheless, we expect the Green function in Schwarzschild spacetime to inherit certain key features, such as a fourfold singular structure manifesting itself through the asymptotic behavior of quasinormal modes. In this way, the Nariai spacetime provides a fertile testing ground for developing insight into the nonlocal part of the self-force on black hole spacetimes.

General relativity is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The deep mystery of dark energy (and possibly even the requirement of cold dark matter), has increased the need for testing modifications to general relativity, as the inference of such otherwise undetected fluids, depends crucially on the theory of gravity. In this work I outline a general scheme for constructing consistent and covariant modifications to the Einstein equations. This framework is such that there is a clear connection between the modification and the underlying field content that produces it. I argue that this is mandatory for distinguishing modifications of gravity from conventional fluids. I give two nontrivial examples, the first of which is a simple metric-based modification of the fluctuation equations for which the background is exact $\Lambda \mathrm{CDM}$ and the second has a Dvali-Gabadadze-Porrati background but differs from it in the perturbations. I present their impact on observations of the cosmic microwave background radiation.

We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axial-vector currents: the vector, induced tensor, axial-vector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with $N_f=2+1$ dynamical domain-wall fermions and Iwasaki gauge actions at $\beta =2.13$, corresponding to a cutoff $a^{-1}=1.73\mathrm{GeV}$, and a spatial volume of $(2.7\mathrm{fm}{)}^3$. The up and down-quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, $0.2<q^2<0.75{\mathrm{GeV}}^2$. The vector and induced tensor form factors are well described by the conventional dipole forms and result in significant underestimation of the Dirac and Pauli mean-squared radii and the anomalous magnetic moment compared to the respective experimental values. We show that the axial-vector form factor is significantly affected by the finite spatial volume of the lattice. In particular in the axial charge, $g_A/g_V$, the finite-volume effect scales with a single dimensionless quantity, $m_{\pi }L$, the product of the calculated pion mass and the spatial lattice extent. Our results indicate that for this quantity, $m_{\pi }L>6$ is required to ensure that finite-volume effects are below 1%.

In order to explore the possible existence of the exotic $0^{--}$ state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the $0^{+-}$ tetraquark operators without derivatives do not exist. The special Lorentz structure of the $0^{--}$ currents forbids the four-quark type of corrections to the spectral density. Now the gluon condensates are the dominant power corrections. None of the seven interpolating currents support a resonant signal. Therefore we conclude that the exotic $0^{--}$ state does not exist below 2 GeV, which is consistent with the current experimental observations.

We study the evolution of massive mixed Dirac and Majorana neutrinos in matter under the influence of a transversal magnetic field. The analysis is based on relativistic quantum mechanics. We solve exactly the evolution equation for relativistic neutrinos, find the neutrino wave functions, and calculate the transition probability for spin-flavor oscillations. We analyze the dependence of the transition probability on the external fields and compare the cases of Dirac and Majorana neutrinos. The evolution of Majorana particles in vacuum is also studied and correction terms to the standard oscillation formula are derived and discussed. As a possible application of our results we discuss the spin-flavor transitions in supernovae.

We comment on the calculational mistake in the paper “Modeling galaxy halos using dark matter with pressure” by Somnath Bharadwaj and Sayan Kar. The authors made a mistake while calculating the metric, which led to an overestimate of the deflection angle of light passing through the halos for $-1<w_r<-0.5$ and an underestimate of the deflection angle for $-0.5<w_r<0$. In addition, the solution for $w_r>0$ should not exist. Although the Bharadwaj-Kar solution should be corrected, it appears that the characteristics of the deflection angle under the supposed nonconventional, nonideal fluid equation of state for the dark matter halo remain sensitive to the impact parameter and may be verifiable through observations.

We evaluate at one loop the self-energies for the $W$, $Z$ mesons in the electroweak model where the gauge group is nonlinearly realized. In this model the Higgs boson parameters are absent, while a second mass parameter appears together with a scale for the radiative corrections. We estimate these parameters in a simplified fit on leptons and gauge bosons data. We check physical unitarity and the absence of infrared divergences. Landau gauge is used. As a reference for future higher order computations, the regularized $D$-dimensional amplitudes are provided. Eventually the limit $D\to 4$ is taken on physical amplitudes.

We investigate the behavior of parallel Faddeev-Hopf vortices under energy minimization in a system with physically relevant, but unusual boundary conditions. The homotopy classification is no longer provided by the Hopf invariant, but rather by the set of integer homotopy invariants proposed by Pontrjagin. The nature of these invariants depends on the boundary conditions. A set of tightly wound parallel vortices of the usual Hopfion structure is observed to form a bunch of intertwined vortices or unwind completely, depending on the boundary conditions.

We explore the space of static solutions of the recently discovered three-dimensional “new massive gravity” (NMG), allowing for either sign of the Einstein-Hilbert term and a cosmological term parametrized by a dimensionless constant $\lambda$. For $\lambda =-1$ we find black hole solutions asymptotic (but not isometric) to the unique (anti) de Sitter [(A)dS] vacuum, including extremal black holes that interpolate between this vacuum and $(\mathrm{A}){\mathrm{dS}}_2\times S^1$. We also investigate unitarity of linearized NMG in (A)dS vacua. We find unitary theories for some dS vacua, but (bulk) unitarity in AdS implies negative central charge of the dual conformal field theories (CFT), except for $\lambda =3$ where the central charge vanishes and the bulk gravitons are replaced by “massive photons.” A similar phenomenon is found in the massless limit of NMG, for which the linearized equations become equivalent to Maxwell’s equations.

To cure the lack of predictive power of general relativity, Geroch proposed to complete the theory with an additional postulate that only “hole-free” spacetimes are permitted. This postulate (or, rather, that obtained from it by some disambiguating) seems physically well-founded and at the same time appropriately restrictive. I show, however, that it is too strong—it prohibits even the Minkowski space.

We produce numerical evidence that spikes in the mixmaster regime of $G_2$ cosmologies are transient and recurring, supporting the conjecture that the generalized mixmaster behavior is asymptotically nonlocal where spikes occur. Higher-order spike transitions are observed to split into separate first-order spike transitions.