String-inspired Chern–Simons modified gravity in four dimensions

Field equations of the Chern–Simons modified gravity in four dimensions are obtained by a truncation of the field equations of the low energy effective string models with first order corrections in the string constant included.     

Repulsive gravity near naked singularities and point massive particles

We summarize the parallel session B4: ‘Analytic approximations, perturbation theory, effective field theory methods and their applications’ and the joint session B2/B4: ‘Approximate solutions to Einstein equations: Methods and Applications’, of the GR20 & Amaldi10 conference in Warsaw, July 2013. The contributed talks reported significant advances on various areas of research in gravity.     

Relativistic dynamics of interacting point particles: Central position of the Wheeler-Feynman scheme

The Wheeler-Feynman (WF) relativistic theory of interacting point particles, generalized by acceptance of an arbitrary spacelike interaction, is shown to possess a privileged status, reminiscent of the central force interactions occurring in Newtonian mechanics. This scheme is shown to be isomorphic to the classical one of the statics of interacting flexible current-carrying wires obeying the Ampère-Laplace (AL) formulas: to the tensionT (T ² =const) of the wire corresponds the momentum-energy pⁱ (p_ipⁱ=–c²m²) of the particle; to the Laplace linear force density –iH×dr corresponds the Lorentz force QH^ij dr_j; to the Laplace potential ir^–1 dr corresponds the WF potential Q(r²) drⁱ, etc. Among the differences, there is self-action in the AL scheme and no self-action in the WF scheme. A stationary energy principle in the AL scheme is isomorphic to Fokker's stationary action principle in the WF scheme.     

Strongly interacting particles with strongly singular potentials

A statistical system of particles is considered for which interaction potentials are strongly singular so that the standard perturbation theory cannot be used. A regular procedure for constructing a mass operator is suggested, having no ultraviolet divergences and giving the possibility of finding corrections for any approximation chosen. In this procedure, the divergences connected with the potential singularity are eliminated with the help of a smoothing function, for which a simple equation is given and whose properties are analyzed both analytically and numerically. Two effective regularization methods are formulated, eliminating divergences occurring while iterating propagator equations. A continuous iterative procedure is invented for calculating observable quantities and the fast convergence conditions for this procedure are shown to be equivalent to the fixed-point conditions.     

Superweakly interacting massive particles

We investigate a new class of dark matter: superweakly interacting massive particles (super-WIMPs). As with conventional WIMPs, super-WIMPs appear in well motivated particle theories with naturally the correct relic density. In contrast to WIMPs, however, super-WIMPs are impossible to detect in all conventional dark matter searches. We consider the concrete examples of gravitino and graviton cold dark matter in models with supersymmetry and universal extra dimensions, respectively, and show that super-WIMP dark matter satisfies stringent constraints from big bang nucleosynthesis and the cosmic microwave background.     

Evolution of mixed particles interacting with classical sources

Systems of scalar and spinor particles that underwent mixing and which originated from external classical sources were investigated. Particle wave functions that take exactly into account external sources were obtained on the basis of solving Lorentz-invariant wave equations in four-dimensional space. Sources localized in space that emit harmonic radiation were considered. It was found that, owing to the presence of vacuum mixing, the scalar and spinor fields in question might oscillate—that is, go over to one another. It was shown that this phenomenon was analogous to neutrino flavor oscillations in a vacuum, since the calculated transition probabilities were coincidentwith their counterparts for neutrino oscillations. The situation of an arbitrarymassmatrix (that is, that which involved bothDirac andMajoranamass terms) was studied for the case of spinor-field evolution. The possibility of the appearance of antiparticles in a beam that originally involved only particles was analyzed. The question of whether the use of this method in describing neutrino flavor oscillations is legitimate was studied.     

Nonrotating cosmic strings interacting with gravitational waves in Einstein-Maxwell-dilaton gravity

We present methods for the construction of exact diagonal cylindrically symmetric solutions in a four dimensional low energy limit of string theory, the Einstein-Maxwell-dilaton gravity. The methods allow us to generate exact string backgrounds from known solutions to the equations of Einstein or Einstein gravity coupled to a massless scalar field. We also give and analyze explicit examples of such solutions. It is shown that they are free of curvature singularities,(quasi)regular on the axis of symmetry, asymptotically flat and describe nonrotating cosmic strings interacting with gravitational, dilaton and electromagnetic waves.     

An interacting geometry model and induced gravity

We propose the theory of quantum gravity with interactions introduced by topological principle. The fundamental property of such a theory is that its energy-momentum tensor is a BRST anticommutator. Physical states are elements of the BRST cohomology group. The model with only topological excitations, introduced recently by Witten, is discussed from the point of view of the induced gravity program. We find that the mass scale is induced dynamically by gravitational instantons. The low-energy effective theory has gravitons, which occur as the collective excitations of geometry, when the metric becomes dynamical. Applications of cobordism theory to quantum gravity are discussed.This essay received the second award from the Gravity Research Foundation for the year 1988.—Ed.     

Brownian motion in inhomogeneous media and with interacting particles

Brownian motion in media with a space-dependent temperature and density is described by Langevin equations in phase space. Elimination of the velocity shows that diffusion inx-space cannot in general be characterized by a single diffusion parameter, nor can space-dependence always be accounted for by mere assignment of some sense of stochastic integration to the Langevin equation which has been reduced as in the homogeneous case. Steady solutions of the resulting equations agree with thermodynamics. Interactions between Brownian particles (giving rise to nonlinear Fokker-Planck equations) lead to a generalization of Einstein's relation.Work supported by the Swiss National Science Foundation     

New developments in the theory of gravity interacting with quantized fields

Renormalization in the theory of a quantized scalar field interacting with the classical Einstein gravitational field is discussed. The scalar field obeys the generalization of the Klein-Gordon equation which is conformally invariant in the limit of vanishing mass. A generalized Kasner metric corresponding to an anisotropic expansion of the universe is considered. Results obtained in collaboration with S.A. Fulling and B.L. Hu are described, which show explicitly how the infinities appearing in the expectation value of the energy-momentum tensor can be absorbed through renormalization of the cosmological constant and the coefficients of a quadratic tensor appearing in a slightly generalized form of the Einstein equation. There is also a finite renormalization of the gravitational constant.     

Spinning particles in scalar-tensor gravity

We develop a new model of a spinning particle in Brans-Dicke spacetime using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.     

Equilibrium fluctuations for interacting Brownian particles

We consider an infinitely extended system of Brownian particles interacting by a pair force-gradV. Their initial distribution is stationary and given by the Gibbs measure associated with the potentialV with fugacityz. We assume thatV is symmetric, finite range, three times continuously differentiable, superstable, and positive and that the fugacity is small in the sense that 0z0.28/edq(1-e ^–V(q)). In addition a certain essential self-adjointness property is assumed. We prove then that the time-dependent fluctuations in the density on a spatial scale of order ^–1 and on a time scale of order ^–2 converge as 0 to a Gaussian field with covariance dqg(q)(e ^(/2)|t| f)(q) withp the density and the compressibility.     

Dynamic fragmentation of solid particles interacting with a rigid barrier

Fragmentation of small solid particles as a result of collision with a rigid barrier is considered. It is shown that the application of the Griffith energy approach to dynamic fracture is characterized by specific surface energy differing from its value determined from static tests. The existence of the threshold fragmentation velocity is established and the method for its prediction is proposed. The method for experimental estimation of the fracture incubation time is also proposed.