We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type $R^{1,2}\times {\mathrm{M}}_8$ and ${\mathrm{AdS}}_3\times {\mathrm{M}}_8.$ We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G structures and their intrinsic torsion. These equations may be interpreted as calibration conditions for a static “dyonic” M-brane, that is, an M5-brane with a self-dual three-form turned on. When the electric flux is turned off we obtain the supersymmetry conditions and non-linear PDEs describing M5-branes wrapped on associative and special Lagrangian three-cycles in manifolds with $G_2$ and $\mathrm{SU}\left(3\right)\mathrm{}$ structures, respectively. As an illustration of our formalism, we recover the 1/2 BPS dyonic M-brane, and also construct some new examples.

Self-phase modulation of spherical gravitational wave packets propagating in a flat space-time in the presence of a tenuous distribution of matter is considered. Analogies with respect to similar effects in nonlinear optics are explored. Self-phase modulation of waves emitted from a single source can eventually lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range. An explicit criterion for the occurrence of a significant spectral energy dilution is established.

Many alternative formulations of Einstein’s evolution have lately been examined in an effort to discover one that yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations, we instead develop analytic tools to discover which formulations are particularly ill behaved. Specifically, we examine the growth of approximate (geometric-optics) solutions, studied only in the future domain of dependence of the initial data slice (e.g., we study transients). By evaluating the amplification of transients a given formulation will produce, we may therefore eliminate from consideration the most pathological formulations (e.g., those with numerically unacceptable amplification). This technique has the potential to provide surprisingly tight constraints on the set of formulations one can safely apply. To illustrate the application of these techniques to practical examples, we apply our technique to the 2-parameter family of evolution equations proposed by Kidder, Scheel, and Teukolsky, focusing in particular on flat space (in Rindler coordinates) and Schwarzschild background (in Painlevé-Gullstrand coordinates).

In this paper we consider only the possibility of the generation of the linear polarization of the electromagnetic field (EMF) due to the quantum effects of the EMF in an anisotropic Bianchi type I model. We consider the generation of the polarization of the EMF under an idealized supposition that the medium is transparent. It has been established that the quantum effects of the EMF in the external gravitational field of the anisotropic Bianchi type I model provide a contribution to the degree of polarization of the cosmic microwave background in quadrupole harmonics. The limit of the redshift where the quantum effects are essential is derived.

We study and look for similarities between the response rates $R^{\mathrm{dS}}{(a}_0,\Lambda )$ and $R^{\mathrm{SdS}}{(a}_0,\Lambda ,M)$ of a static scalar source with constant proper acceleration $a_0$ interacting with a massless, conformally coupled Klein-Gordon field (i) in de Sitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the de Sitter cosmological horizon and (ii) in Schwarzschild–de Sitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where $\Lambda$ is the cosmological constant and M is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of de Sitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild–de Sitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that $R^{\mathrm{dS}}{(a}_0,\Lambda )$ and $R^{\mathrm{SdS}}{(a}_0,\Lambda ,M)$ do not coincide in general, but tend to each other when $\overrightarrow{\Lambda }0$ or $a_0\to \infty .$ Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.

We propose that stretched horizons can be described in terms of a gas of noninteracting quasiparticles. The quasiparticles are unstable, with a lifetime set by the imaginary part of the lowest quasinormal mode frequency. If the horizon arises from an AdS-CFT style duality the quasiparticles are also the effective low-energy degrees of freedom of the finite-temperature CFT. We analyze a large class of models including Schwarzschild black holes, nonextremal $\mathrm{D}p$-branes, the rotating BTZ black hole and de Sitter space, and we comment on degenerate horizons. The quasiparticle description makes manifest the relationship between entropy and area.

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A $\Gamma$-law equation of state $P=\left(\Gamma -1\right)\rho \varepsilon$ is adopted, where P, $\rho ,$ $\varepsilon ,$ and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take $\Gamma =2\mathrm{}$ and the baryon rest-mass ratio $Q_M$ to be in the range 0.85–1. The typical grid size is $\mathrm{}(633,633,317)\mathrm{}$ for $\mathrm{}(x,y,z).$ We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest mass of the system is more than $\sim 1.7$ times of the maximum allowed rest mass of spherical neutron stars, a black hole is formed after the merger, irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range $Q_M=0.85\mathrm{}–1.$

Quantum fluctuations of the light cone are examined in a four-dimensional spacetime with two parallel planes. Both the Dirichlet and the Neumann boundary conditions are considered. In all the cases we have studied, quantum light cone fluctuations are greater where the Neumann boundary conditions are imposed, suggesting that quantum light cone fluctuations depend not only on the geometry and topology of the spacetime as has been argued elsewhere but also on boundary conditions. Our results also show that quantum light cone fluctuations are larger here than that in the case of a single plane. Therefore the confinement of gravitons in a smaller region by the presence of a second plane reinforces the quantum fluctuations and this can be understood as a consequence of the uncertainty principle.

Transforming Penrose’s intuitive picture of a strong cosmic censorship principle—that generically forbids the appearance of locally naked space-time singularities—into a formal mathematical proof, remains at present, one of the most outstanding unsolved mathematical problems from the theory of gravitational collapse. Part of the difficulty lies in the fact that we do not possess yet a clear-cut understanding of the hypothesis needed for the establishment of some sort of strong cosmic censorship theorem. What we have is a selected list of solutions, which at first sight seem to go against cosmic censorship, but at the end they fail in some way. However, the space of solutions of Einstein’s field equations is vast. In this article, we plan to increase one’s intuition by establishing a link between certain inequalities for Cauchy-horizon stability and a set of generic conditions, such as a reasonable equation of state, which determines whether or not the space-time is asymptotically flat, an energy condition, and a hypothesis over the class of metrics on which Einstein’s field equations ought to be solved to ensure strong cosmic censorship inside black holes. With these tools in hand we examine the Cauchy-horizon stability of the theory created by Born and Infeld, whose action principle has been used as a prototype in superstring theory, and the singularity-free Bardeen black-hole model.

We investigate a stabilization of extra dimensions in a ten-dimensional Kaluza-Klein theory and type IIB supergravity. We assume $\left(\mathrm{A}\right){\mathrm{dS}}_5\times {\mathrm{S}}^5$ compactification, and calculate quantum effects to find an effective potential for the radius of internal space. The effective potential has a minimum, and if the universe is created on the top of the potential hill, the universe evolves from ${\mathrm{dS}}_5$ to ${\mathrm{AdS}}_5$ after exponential expansion. The internal space ${\mathrm{S}}^5$ stays small and its radius becomes constant. Our model in type IIB supergravity contains the 4-form gauge field with a classical vacuum expectation value, which is the role of a ten-dimensional cosmological constant. If the universe evolves into anti–de Sitter, the five-dimensional Randall-Sundrum setup with a stabilized dilaton is obtained from the type IIB supergravity model.

The effects that the present accelerating expansion of the Universe has on the size and shape of Lorentzian wormholes and ringholes are considered. It is shown that, quite similarly to how it occurs for inflating wormholes, relative to the initial embedding-space coordinate system, whereas the shape of the considered holes is always preserved with time, their size is driven by the expansion to increase by a factor which is proportional to the scale factor of the Universe. In the case that dark energy is phantom energy, which is not excluded by present constraints on the dark-energy equation of state, that size increase with time becomes quite more remarkable, and a rather speculative scenario is here presented where the big rip can be circumvented by future advanced civilizations by utilizing sufficiently grown up wormholes and ringholes as time machines that shortcut the big-rip singularity.

We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a nonzero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a quasirigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near $r=9M)$ of a Schwarzschild black hole.

We study the properties of the outgoing gravitational wave produced when a nonspinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein’s equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first-order quasilinear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.

Entropy production from scalar decay in the era of low temperatures after neutrino decoupling will change the ratio of the relic neutrino temperature to the CMB temperature, and, hence, the value of $N_{\mathrm{eff}},$ the effective number of neutrino species. Such scalar decay is relevant to reheating after thermal inflation, proposed to dilute massive particles, like the moduli and the gravitino, featuring in supersymmetric and string theories. The effect of such entropy production on the relic neutrino temperature ratio is calculated in a semianalytic manner, and a recent lower bound on this ratio, obtained from the WMAP satellite and 2dF galaxy data, is used to set a lower bound of $\sim 1.5\times {10}^{-23}$ GeV on the scalar decay constant, corresponding to a reheating temperature of about $3.3$ MeV.

We explore cosmological implications of dark matter as massive particles trapped on a brane embedded in a Randall-Sundrum noncompact higher dimension ${\mathrm{AdS}}_5$ space. It is an unavoidable consequence of this cosmology that massive particles are metastable and can disappear into the bulk dimension. Here, we show that a massive dark matter particle (e.g. the lightest supersymmetric particle) is likely to have the shortest lifetime for disappearing into the bulk. We examine cosmological constraints on this new paradigm and show that disappearing dark matter is consistent (at the 95% confidence level) with all cosmological constraints, i.e., present observations of type Ia supernovae at the highest redshift, trends in the mass-to-light ratios of galaxy clusters with redshift, the fraction of x-ray emitting gas in rich clusters, and the spectrum of power fluctuations in the cosmic microwave background. A best $2\sigma$ concordance region is identified corresponding to a mean lifetime for dark matter disappearance of $15<~{\Gamma }^{-1}<~80\mathrm{Gyr}.$ The implication of these results for brane-world physics is discussed.

A common property of popular models of quintessence dark energy is the convergence to a common solution from a large range of the initial conditions. We reexamine the popular inverse power-law model of quintessence (where the common solution is dubbed as the “tracker”) with particular attention to the initial conditions for the field and their influence on the evolution. We find that previously derived limits on the parameters of the potential in this model are valid only in a range of initial conditions. A reasonably sharp boundary lies where the initial energy density of the scalar field is equal to that of the background radiation component. An initial quintessence energy density above this equipartition value leads to a solution that will not have joined the tracker solution by the present epoch. These nontracker solutions possess the property that their present equation of state is very compatible with the observed bounds and independent of the exponent of the potential.

The dynamics of LFRW universes with a massive scalar field is examined where a potential term derived from quantum cosmology is introduced in the equations of motion of the system. This potential term is connected to a repulsive force arising from the equations of Bohmian trajectories in the framework of the de Broglie–Bohm interpretation of quantum cosmology. For a nonzero mass, the dynamics is nonintegrable and chaotic and the quantum potential term creates metastable configurations confined between KAM tori. For certain domains of the parameter space labeled by the scalar field mass and the conserved Hamiltonian, we have nonlinear resonance phenomena that may induce the destruction of KAM tori. This leads to a rapid growth of the scale factor and the scalar field, with the disruption of metastable states and consequent escape of the Universe into inflation. A semianalytical approach to these phenomena is made and possible consequences to structure formation discussed. Also the dynamics connected with the breaking and crossing of homoclinic cylinders present in the phase space of the models is examined, as they induce effective mechanisms of a chaotic exit to inflation for other sets of initial conditions, but with a milder oscillatory behavior of the degrees of freedom.

In this paper we construct an expanding phase with phantom matter, in which the scale factor expands very slowly but the Hubble parameter increases gradually, and assume that this expanding phase could be matched to our late observational cosmology by the proper mechanism. We obtain the nearly scale-invariant spectrum of adiabatic fluctuations in this scenario; different from the simplest inflation and usual ekpyrotic or cyclic scenario, the tilt of the nearly scale-invariant spectrum in this scenario is blue. Although there exists an uncertainty surrounding the way in which the perturbations propagate through the transition in our scenario, which is dependent on the details of possible “bounce” physics, compared with inflation and the ekpyrotic or cyclic scenario, our work may provide another feasible cosmological scenario generating the nearly scale-invariant perturbation spectrum.

In this paper, we describe a way to construct a class of dark energy models that admits late time de Sitter attractor solution. In the canonical scalar and Born-Infeld scalar dark energy models, we show mathematically that a simple sufficient condition for the existence of a late time de Sitter-like attractor solution is that the potentials of the scalar field have a nonvanishing minimum while this condition becomes that the potentials have a nonvanishing maximum for the phantom models. These attractor solutions correspond to an equation of state $w=-1$ and a cosmic density parameter ${\Omega }_{\phi }=1,$ which are important features for a dark energy model that can meet the current observations.