We study classical solutions in the Berenstein-Maldacena-Nastase matrix model. A supersymmetric (1/2 Bogomol’nyi-Prasad-Sommerfield) fuzzy sphere is one of the classical solutions and corresponds to a giant graviton. We also consider other classical solutions, such as a nonsupersymmetric fuzzy sphere and harmonic oscillating gravitons. Some properties of oscillating gravitons are discussed. In particular, oscillating gravitons turn into the usual supergravitons in the limit $\overrightarrow{\mu }0.$ Moreover, we calculate the one-loop effective action around the supersymmetric fuzzy sphere by the use of the background field method and show the quantum stability of the giant graviton. Also, the instability of the nonsupersymmetric fuzzy sphere is proven.

We use the supergravity modes to clarify the role of the prefactor in the light-cone superstring field theory on a pp-wave background. We verify some of the proposals of Constable et al. and give further evidence for the correspondence between $\mathcal{N}=4\mathrm{}$ Super Yang-Mills gauge theory and string theory on a pp-wave. We also consider energy-preserving processes and find that they give a vanishing cubic interaction Hamiltonian matrix.

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in $1/F,$ where $F\sim 1/g\left(m\right)\mathrm{}$ for $m\gg \Lambda$ while $F\sim (m/\Lambda {)}^{\alpha }$ for $m\lesssim \Lambda ,$ $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of F which corresponds to reach unambiguously the strong coupling infrared regime near $\overrightarrow{m}0,$ which can define certain “nonperturbative” quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by reevaluating, from purely perturbative information, the $O\left(N\right)\mathrm{}$ Gross-Neveu model mass gap, known for arbitrary N from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.

Spontaneous global symmetry breaking of $O\left(3\right)\mathrm{}$ scalar field gives rise to point-like topological defects, global monopoles. By taking into account self-gravity, the qualitative feature of the global monopole solutions depends on the vacuum expectation value $v$ of the scalar field. When $v<\mathrm{}\sqrt{1/8\pi },$ there are global monopole solutions which have a deficit solid angle defined at infinity. When $\sqrt{1/8\pi }<~v<\mathrm{}\sqrt{3/8\pi },$ there are global monopole solutions with the cosmological horizon, which we call the supermassive global monopole. When $v>~\sqrt{3/8\pi },$ there is no nontrivial solution. It was shown that all of these solutions are stable against the spherical perturbations. In addition to the global monopole solutions, the de Sitter solutions exist for any value of $v.\mathrm{}$ They are stable against the spherical perturbations when $v<~\sqrt{3/8\pi },$ while unstable for $v>\mathrm{}\sqrt{3/8\pi }.$ We study polar perturbations of these solutions and find that all self-gravitating global monopoles are stable even against polar perturbations, independently of the existence of the cosmological horizon, while the de Sitter solutions are always unstable.

A family of theories which are dual to the massive spin two Fierz-Pauli field $h_{\mu \nu },$ both free and coupled to external sources, is constructed in terms of a $T_{\left(\mu \nu \right)\sigma }$ tensor. The dualization method, a purely Lagrangian approach, is based on a first order parent Lagrangian, from which the dual partners are generated.

We consider (3+1)-dimensional, Dirac electrons of arbitrary mass, propagating in the presence of electric and magnetic fields which are both parallel to the $x^3$ axis. The magnetic field is constant in space and time whereas the electric field depends arbitrarily upon the light-cone time parameter $x^{+}{=(x}^0{+x}^3)/\sqrt{2}.$ We present an explicit solution to the Heisenberg equations for the electron field operator in this background. The electric field results in the creation of electron-positron pairs. We compute the expectation values of the vector and axial vector currents in the presence of a state which is free vacuum at $x^{+}=0.\mathrm{}$ Both current conservation and the standard result for the axial vector anomaly are verified for the first time ever in (3+1)-dimensional light-cone QED. An interesting feature of our operator solution is the fact that it depends in an essential way upon operators from the characteristic at $x^{-}=-L,$ in addition to the usual dependence upon operators at $x^{+}=0.\mathrm{}$ This dependence survives even in the limit of infinite L. Ignoring the $x^{-}$ operators leads to a progressive loss of unitarity, to the violation of current conservation, to the loss of renormalizability, and to an incorrect result for the axial vector anomaly.

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged scalars in the combined theory of general relativity and scalar QED. The combined theory is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the non-analytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude, which are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two charged scalars. The result is discussed in relation to experimental verifications.

We derive the explicit values of all regularization parameters (RP) for a scalar particle in an arbitrary geodesic orbit around a Schwarzschild black hole. These RP are required within the previously introduced mode-sum method for calculating the local self-force acting on the particle. In this method, one first calculates the (finite) contribution to the self-force due to each individual multipole mode of the particle’s field, and then applies a certain regularization procedure to the mode sum, involving the RP. The explicit values of the RP were presented in a recent paper [L. Barack et al., Phys. Rev. Lett. 88, 091101 (2002)]. Here we give the full details of the RP derivation in the scalar case. The calculation of the RP in the electromagnetic and gravitational cases will be discussed in an accompanying paper.

We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived and subsequently specialized to the vacuum case. We first examine the relative motion of two dust shells by focusing on the dynamics of the exterior shell, whereby the problem is reduced to that of a single shell with different active Schwarzschild masses on each side. We then examine the dynamics of shells with nonvanishing tangential pressure p, and show that there are no stable—stationary, or otherwise—solutions for configurations with a strictly linear barotropic equation of state, $p=\alpha \sigma ,$ where $\sigma$ is the proper surface energy density and $\alpha \in (-1,1).$ For arbitrary equations of state, we show that, provided the weak energy condition holds, the strong energy condition is necessary and sufficient for stability. We examine in detail the formation of trapped surfaces, and show explicitly that a thin boundary layer causes the apparent horizon to evolve discontinuously. Finally, we derive an analytical (necessary and sufficient) condition for neighboring shells to cross, and compare the discrete shell model with the well-known continuous Lemaître-Tolman-Bondi dust case.

$\mathrm{}(2+1)\mathrm{}$-dimensional anti–de Sitter space has been the subject of much recent investigation. Studies of the behavior of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological identification of AdS isometries. In this paper, we present a new configuration of two orbiting massive point particles that leads to an “eternal” time machine, where closed timelike curves fill the entire space. In contrast with previous solutions, this configuration has no event or chronology horizons. Another interesting feature is that there is no lower bound on the relative velocities of the point masses used to construct the time machine; as long as the particles exceed a certain mass threshold, an eternal time machine will be produced.

The interaction energy between two black holes at a large separation distance is calculated. The first term in the expansion corresponds to the Newtonian interaction between the masses. The second term corresponds to the spin-spin interaction. The calculation is based on the interaction energy defined on the two black holes’ initial data. No test particle approximation is used. The relation between this formula and cosmic censorship is discussed.

We show that the redshift of pressureless matter density due to the expansion of the universe generically induces small oscillations in the stabilized radius of extra dimensions (the radion field). The frequency of these oscillations is proportional to the mass of the radion and can have interesting cosmological consequences. For very low radion masses $m_b\left[m_b\sim \right(10\mathrm{}–{100)H}_0\simeq {10}^{-32}\mathrm{eV}]$ these low frequency oscillations lead to oscillations in the expansion rate of the universe. The occurrence of acceleration periods could naturally lead to a resolution of the coincidence problem, without need of dark energy. Even though this scenario for low radion mass is consistent with several observational tests it has difficulty meeting fifth force constraints. If viewed as an effective Brans-Dicke theory it predicts $\omega =-1+1/D$ $(D$ is the number of extra dimensions), while experiments on scales larger than 1 mm imply $\omega >2500.\mathrm{}$ By deriving the generalized Newtonian potential corresponding to a massive toroidally compact radion we demonstrate that Newtonian gravity is modified only on scales smaller than $m_b^{-1}.$ Thus, these constraints do not apply for $m_b>{10}^{-3}\mathrm{eV}$ (high frequency oscillations) corresponding to scales less than the current experiments (0.3 mm). Even though these high frequency oscillations cannot resolve the coincidence problem they provide a natural mechanism for dark matter generation. This type of dark matter has many similarities with the axion.

The polarized Gowdy ${\mathbf{T}}^3$ vacuum spacetimes are characterized, modulo gauge, by a “point particle” degree of freedom and a function φ that satisfies a linear field equation and a nonlinear constraint. The quantum Gowdy model has been defined by using a representation for φ on a Fock space F. Using this quantum model, it has recently been shown that the dynamical evolution determined by the linear field equation for φ is not unitarily implemented on F. In this paper, (1) we derive the classical and quantum model using the “covariant phase space” formalism, (2) we show that time evolution is not unitarily implemented even on the physical Hilbert space of states $\mathcal{H}\subset \mathcal{F}$ defined by the quantum constraint, and (3) we show that the spatially smeared canonical coordinates and momenta as well as the time-dependent Hamiltonian for φ are well-defined, self-adjoint operators for all time, admitting the usual probability interpretation despite the lack of unitary dynamics.

We formulate a dynamically triangulated model of three-dimensional Lorentzian quantum gravity whose spatial sections are flat two tori. It is shown that the combinatorics involved in evaluating the one-step propagator (the transfer matrix) is that of a set of vicious walkers on a two-dimensional lattice with periodic boundary conditions and that the entropy of the model scales exponentially with the volume. We also give explicit expressions for the Teichmüller parameters of the spatial slices in terms of the discrete parameters of the 3D triangulations, and reexpress the discretized action in terms of them. The relative simplicity and explicitness of this model make it ideally suited for an analytic study of the conformal-factor cancellation observed previously in Lorentzian dynamical triangulations and of its relation to alternative, reduced phase space quantizations of 3D gravity.

Numerical calculations of the head-on collision of two neutron stars are made using the full Einstein equations. The density of the stars is found to rise well before the stars collide. For comparision, calculations are also made with the spatial part of the metric constrained to be conformally flat. This calculation gives rise to nearly the same compression as the calculation made with the full proper metric. Previously the same type of stellar compression was obtained in neutron star binary hydrodynamic calculations which assumed conformally flat space. As such, this effect is not dependent upon the rotational motion of the stars and is more general. These results lend credence to the compression observed in the simulations of binary neutron stars for which a conformally flat spatial metric was assumed.

Within the framework of a five-dimensional brane world with a stabilized radion, we compute the cosmological perturbations generated during inflation and show that the perturbations are a powerful tool to probe the physics of extra dimensions. While we find that the power spectrum of scalar perturbations is unchanged, we show that the existence of the fifth dimension is imprinted on the spectrum of gravitational waves generated during inflation. In particular, we find that the tensor perturbations receive a correction proportional to ${\mathrm{}\left(\mathrm{HR}\right)\mathrm{}}^2,$ where H is the Hubble expansion rate during inflation and R is the size of the extra dimension. We also generalize our findings to the case of several extra dimensions as well as to warped geometries.

Brane world cosmologies seem to provide an alternative explanation for the present accelerated stage of the Universe with no need to invoke either a cosmological constant or an exotic quintessence component. In this paper we investigate statistical properties of gravitational lenses for some particular scenarios based on this large scale modification of gravity. We show that a large class of such models are compatible with the current lensing data for values of the matter density parameter ${\Omega }_{\mathrm{m}}<~0.94\left(1\sigma \right).\mathrm{}$ If one fixes ${\Omega }_{\mathrm{m}}$ to be $\simeq 0.3,$ as suggested by most of the dynamical estimates of the quantity of matter in the Universe, the predicted number of lensed quasars requires a slightly open universe with a crossover distance between the 4- and 5-dimensional gravities of the order of ${1.76H}_o^{-1}.$

As a simple model for unknown Planck scale physics, we assume that the quantum modes responsible for producing primordial curvature perturbations during inflation are placed in their instantaneous adiabatic vacuum when their proper momentum reaches a fixed high energy scale M. The resulting power spectrum is derived and presented in a form that exhibits the amplitude and frequency of the superimposed oscillations in terms of $H/M$ and the slow roll parameter $\epsilon .$ The amplitude of the oscillations is proportional to the third power of $H/M.\mathrm{}$ We argue that these small oscillations give the lower bound of the modifications of the power spectrum if the notion of free mode propagation ceases to exist above the critical energy scale M.

We discuss the real-space moments of temperature anisotropies in the cosmic microwave background (CMB) due to weak gravitational lensing by intervening large-scale structure. We show that if the probability distribution function of primordial temperature anisotropies is Gaussian, then it remains unchanged after gravitational lensing. With finite resolution, however, nonzero higher-order cumulants are generated both by lensing autocorrelations and by cross-correlations between the lensing potential and secondary anisotropies in the CMB such as the Sunayev-Zel’dovich (SZ) effect. Skewness is produced by these lensing-SZ correlations, while kurtosis receives contributions from both lensing alone and lensing-SZ correlations. We show that if the projected lensing potential is Gaussian, all cumulants of higher order than the kurtosis vanish. While recent results raise the possibility of detection of the skewness in upcoming data, the kurtosis will likely remain undetected.

High resolution N-body simulations have revealed the survival of a considerable substructure within galactic halos. Assuming that the predicted dark matter clumps are composed of annihilating neutralinos, we examine their detectability via atmospheric Cherenkov telescopes (ACTs). Depending on their density profile, individual neutralino clumps should be observable via their γ-ray continuum and line emissions. We find that the continuum signal is the most promising signal for detecting a neutralino clump, being significantly stronger than the monochromatic signals. Limits from the line detectability can help lift degeneracies in the supersymmetric (SUSY) parameter space. We show that by combining the observations of different mass clumps, ACTs can explore most of the SUSY parameter space. ACTs can play a complementary role to accelerator and γ-ray satellite limits by exploring relatively large neutralino masses and less concentrated clumps. We develop a strategy for dark matter clump studies by future ACTs based on VERITAS specifications and encourage the development of techniques to identify primaries. This can reduce the background by an order of magnitude.