Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

Homotopy Approach to Quantum Gravity

Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.     

Field Equations and Conservation Laws Derived from the Generalized Einstein’s Lagrangian Density for a Gravitational System and Their Influences upon Cosmology

Through discussions on the fundamental properties of the generalized Einstein’s Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein’s field equations and the Lorentz and Levi-Civita’s conservation laws are systematically studied. The theory of cosmology founded on them is discussed in detail and some new properties and new effects of the cosmos are deduced; these new properties and new effects could be tested via future experiments and observations.     

Classical tests of general relativity in the Newtonian limit of the Schwarzschild–de Sitter spacetime

Recently it has been shown that despite previous claims the cosmological constant affects light bending. In the present article we study light bending and the advance of Mercury’s perihelion in the context of the Newtonian limit of the Schwarzschild–de Sitter spacetime employing the special relativistic equivalence of mass and energy. In both cases, up to a constant factor, we find the same results as in the full general relativistic treatment of the same phenomena. These approximate and intuitive arguments demonstrate clearly what effects should have been expected from the presence of Λ in the general relativistic treatment of these phenomena.     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.     

Quantum Circuits and Schr?dinger’s Cat States

Quantum systems that are confined to circuit geometries are called quantum circuits. Macroscopic superconducting circuits are quantum circuits which can be modelled using a Quantisation by Parts scheme based on the macroscopic wave function approach of Feynman. This paper studies the circuit composed of an input wire and an output plate. We find that in order to achieve a consistent theory of supercurrent flow we have to generalize the quantisation by parts scheme to quantise in a path space. The generalized theory predicts a current flow down the wire into the plane. In addition to a current flowing radially outwards in the plane, the theory allows a circulating current round the origin. Strikingly, the circulating current can flow clockwise or anti-clockwise in such a way as to generate a magnetic moment of magnitude half of a Bohr magneton for an orbiting electron in an atom and a magnetic flux half that of the magnetic flux quantum of a superconducting ring. There is also the possibility of a macroscopic superposition of the two states of opposing circulating currents resembling a Schr?dinger’s cat situation. Furthermore, we outline a setup involving an external magnetic field that may allow experimental tests of the theory.     

Heavy ion collisions and black hole dynamics

Relativistic heavy ion collisions create a strongly coupled quark-gluon plasma. Some of the plasma’s properties can be approximately understood in terms of a dual black hole. These properties include shear viscosity, thermalization time, and drag force on heavy quarks. They are hard to calculate from first principles in QCD. Extracting predictions about quark-gluon plasmas from dual black holes mostly involves solving Einstein’s equations and classical string equations of motion. AdS/CFT provides a translation from gravitational calculations to gauge theory predictions. The gauge theory to which the predictions apply is = 4 super-Yang-Mills theory. QCD is different in many respects from super-Yang-Mills, but it seems that its high temperature properties are similar enough to make some meaningful comparisons. Third Award in the 2007 Essay Competition of the Gravity Research Foundation.     

Increasing the frequency resolution in the processing of acoustic signals by sliding complex weighted averaging

We investigated the possibilities of estimating the transient impedance of an emitter and receiver in a free field, and we present our results, which are based on sliding complex weighted averaging of the frequency dependence of emitter and receiver’s transient impedance in a nonanechoic bath. We show that the procedure makes it possible to reduce reflection effects and to form free-field conditions in baths with various reflections that differ sharply in shape and many times in size. We suggest a procedure of repeat use of sliding complex weighted averaging together with spectrometry of reflection functions, which makes it possible to increase the frequency resolution of the method.     

In search of a resolution of Bell’s paradox

It is shown that the violations of Bell’s inequalities observed in optical experiments admit an adequate explanation, on the basis of a model employing four-dimensional joint probabilities, that is consistent with a local hidden-variable theory. For a true experimental demonstration of Bell’s paradox, it is necessary to take account of individual photocounts in the averaging. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 294–296 (25 August 1996)     

Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.     

Quantum gravity: yesterday and today

Bryce DeWitt was one of the great pioneers of quantum gravity. This unpublished lecture gives his recent views on the topic, which we believe will be of great interest not only to researchers involved in modern attempts to quantize Einstein’s theory, but also to a much wider audience. It is the first installment of a book “The Pursuit of Quantum Gravity 1946–2004; Memoirs of Bryce DeWitt” that Cecile DeWitt is preparing. We would like to thank her for the permission to publish this lecture separately in General Relativity and Gravitation. Readers who have unpublished material such as letters from Bryce, and would be willing to send copies to Cecile, are hereby invited to do so. She would be very grateful. G.F.R. Ellis, H. Nicolai (Editors-in-chief). This article was found in Bryce’s files without references and without an indication of its purpose. References and the name of a previously anonymous student have been supplied by Cecile DeWitt and Brandon DiNunno. Bryce DeWitt (1923–2004). An erratum to this article can be found at     

Complex magnetic susceptibility of uniaxial superparamagnetic particles in a strong static magnetic field

The magnetic relaxation of a system of single-domain ferromagnetic particles in the presence of a strong static magnetic field directed at an arbitrary angle relative to the particle anisotropy axis is investigated. A system of linear difference-differential equations for the moments (averaged spherical harmonics) is derived without recourse to the Fokker-Planck equation by averaging Gilbert’s equations with a fluctuating field. An exact solution (in terms of matrix continuous fractions) is found for this system. The relaxation times and spectra of the complex magnetic susceptibility are calculated. Fiz. Tverd. Tela (St. Petersburg) 40, 1642–1649 (September 1998)     

Soaring interfaces, vortices and vortex systems inside the internal waves wake past the horizontally moving cylinder in a continuously stratified fluid

The flow pattern around a horizontal cylinder towed at constant velocity along isopycnic plane in a continuously stratified liquid is visualized by conventional techniques of “Vertical slit-Foucault’s knife”, “Maksoutov’s slit-thread” and “horizontal slit-regular grating”. Using sensitive high-resolution methods allows detail studying such component of stratified flow structures as soaring interfaces, singular soaring vortices and vortex systems, which arise directly inside the internal waves field past the cylinder. These flow elements having high level of vorticity are separated from the downstream wake by a strip of fluid without any small-scale inhomogeneities. Formation of singular vortex dipoles on leading edges of soaring interfaces is investigated in details in a wide range of flow parameters.     

Rotating cylindrically symmetric Kaluza-Klein fluid model

Kaluza-Klein field equations for stationary cylindrically symmetric fluid models in standard Einstein theory are formulated and a set of physically viable solutions is reported. This set is believed to be the first such Kaluza-Klein solutions and it includes the Kaluza-Klein counterpart of Davidson’s solution describing spacetime of a perfect fluid in rigid rotation about a regular axis.     

Gravity: the inside story

It is well known that one could determine the kinematics of gravity by using the Principle of Equivalence and local inertial frames. I describe how the dynamics of gravity can be similarly understood by suitable thought experiments in a local Rindler frame. This approach puts in proper context several unexplained features of gravity and describes the dynamics of spacetime in a broader setting than in Einstein’s theory. First Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Parton energy loss due to synchrotron-like gluon emission

A quasiclassical theory of the synchrotron-like gluon radiation has been developed. The calculations show that the parton energy loss due to the synchrotron gluon emission may be important in the jet quenching phenomenon if the plasma instabilities generate a sufficiently strong chromomagnetic field. The resulting gluon spectrum disagrees with that obtained by Shuryak and Zahed within the Schwinger’s proper time method. The article is published in the original.     

On the low-frequency sound scattering in a moving microinhomogeneous medium

The Rayleigh law that governs low-frequency sound attenuation due to the scattering by inhomogeneities in a microinhomogeneous medium is generalized to the case of particles moving in a flow or falling under gravity. Corrections to the scattering’s cross section that adjust the Rayleigh law to the case of a potential flow around inhomogeneities are calculated. It is shown that, when microinhomogeneities are moving in a viscous medium, the characteristics of discrete scatterers may considerably deviate from the Rayleigh law. Based on the data on the velocity and size distribution of falling drops of water in air, refinements are proposed for the laws of low-frequency sound scattering by rain.     

Dynamic problems of composite mechanics

A procedure for applying Green’s tensor method to the averaging of dynamic problems in the theory of elasticity of nonhomogeneous solids with both periodic and nonperiodic structures is presented.     

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of ‘poetic language’.