A golden age of general relativity? Some remarks on the history of general relativity

This article deals with the concepts “renaissance” and “low water mark between 1925 and 1955” of general relativity suggested in the literature. By empirical data, it is shown that no such period did exist. Research on general relativity continued continuously since the 1920s interrupted only by the second world war. On a broad scale, research on general relativity started only after 1945.     

Classical mechanics via general relativity and Maxwell’s theory: a bit of magic

In the 1950’s Herman Bondi observed that a very effective way to study gravitational radiation was to use null surfaces as part of the coordinate system for analyzing the Einstein (Einstein–Maxwell) equations. A particular class of such surfaces, (referred to as Bondi null surfaces) with their associated null tetrad, has now been the main tool for this analysis for many years; their use—until recently—has been almost ubiquitous. Several years ago we realized that there was an attractive alternative to the use of Bondi coordinates, namely to use coordinates (in the asymptotic null future space–time region) that were as close to ordinary flat-space light-cones as possible—very different from Bondi surfaces. There were initially serious impediments to this program: these new null surfaces (referred to as asymptotically shear-free surfaces, ASF) were determined by solving a non-linear differential equation (the “good-cut” equation) whose solutions were most often complex. Eventually these problems were overcome and the program was implemented. In a series of papers, using the ASF null surfaces to study the asymptotically flat Einstein (or Einstein–Maxwell) equations, a variety of surprising (strange) results were obtained. Using only the Einstein and Maxwell equations, we found a large number of the basic relations of classical mechanics. They included very detailed conservation laws, well know kinematic relations and dynamic equations and even the Abraham–Lorentz–Dirac radiation reaction force and the rocket force. As interesting as these were, they came with a serious enigma. These relations from classical mechanics had no relationship with the physical space–time. The space for the action of these relations was the parameter space of solutions of the good-cut equation—a complex space, known as H-space. The enigma—what possible relationship did these standard appearing classical relations have with physical space–time? It is the purpose of this work to establish such a relationship—objects in H-space are related to structures in physical space–time. For example, a complex world-line in H-space becomes in physical space–time an asymptotically shear-free null geodesic congruence where its twist describes its intrinsic spin and if charged, its magnetic dipole.     

Von Neumann’s growth model: Statistical mechanics and biological applications

We review recent work on the statistical mechanics of Von Neumann’s growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann’s model can be helpful in uncovering functional organization principles of cell energetics.     

Von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.     

Carl Neumann’s Contributions to Electrodynamics

I examine the publications of Carl Neumann (1832–1925) on electrodynamics, which constitute a major part of his work and which illuminate his approach to mathematical physics. I show how Neumann contributed to physics at an important stage in its development and how his work led to a polemic with Hermann Helmholtz (1821–1894). Neumann advanced and extended the ideas of the Königsberg school of mathematical physics. His investigations were aimed at founding a mathematically exact physical theory of electrodynamics, following the approach of Carl G.J. Jacobi (1804–1851) on the foundation of a physical theory as outlined in Jacobis lectures on analytical mechanics. Neumanns work also shows how he clung to principles that impeded him in appreciating and developing new ideas such as those on field theory that were proposed by Michael Faraday (1791–1867) and James Clerk Maxwell (1831–1879).Karl-Heinz Schlote works as a historian of mathematics in the Arbeitsgruppe für Geschichte der Naturwissenschaften und Mathematik at the Sächsische Akademie der Wissenschaften in Leipzig, Germany.     

Von Neumann Entropy of an Electron in One-Dimensional Determined Potentials

By using the measure of von Neumann entropy, we numerically investigate quantum entanglement of an electron moving in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. The delocalized and localized eigenstates can be distinguished by von Neumann entropy of the individual eigenstates.There are drastic decreases in von Neumann entropy of the individual eigenstates at mobility edges. In the curve of the spectrum averaged von Neumann entropy as a function of potential parameter λ, a sharp transition exists at the metal-insulator transition point λc = 2. It is found that the von Neumann entropy is a good quantity to reflect localization and metal-insulator transition.     

Gravitational collapse of spherically symmetric stars in noncommutative general relativity

Gravitational collapse of a class of spherically symmetric stars is investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with gravitational collapse.     

The Poincaré group as the symmetry group of canonical general relativity

This work reconsiders the formulation, due to Regge and Teitelboim, of the phase space approach to general relativity in the asymptotically flat context, phrasing it in the language of symplectic geometry. The necessary boundary conditions at spatial infinity are spelled out in detail. Precise meaning is given to the statement that, as a result of these boundary conditions, the Poincaré group acts as a symmetry group on the phase space of general relativity. This situation is compared with the spi-picture of Ashtekar and Hansen, where a larger asymptotic symmetry group is obtained.     

Standard general relativity from Chern–Simons gravity

Chern–Simons models for gravity are interesting because they provide a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been its perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding “anomalous” Gauss–Bonnet constraints drop out from the Chern–Simons action. To achieve this goal, both the Lie algebra g$\mathfrak{g}$ and the symmetric g$\mathfrak{g}$-invariant tensor that define the Chern–Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite Abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.     

Total conserved charges of Kerr-NUT spacetimes using Poincaré version of teleparallel equivalent of general relativity

Total conserved charges of several axially symmetric tetrad spacetimes generating Kerr-NUT metric are calculated by using the approach of invariant conserved currents. Certain tetrads give the known values, while others give unusual charges and divergent quantities. Therefore, regularized expressions are employed to get the known form of conserved charges.     

L ü $\ddot {u}$ der Rule,Von Neumann Rule and Cirelson’s Bound of Bell CHSH Inequality

International Journal of Theoretical Physics - In Budroni and Emary (Phys. Rev. Lett. 113, 050401, 2014) the authors have shown that instead of L $\ddot {u}$ der rule, if degeneracy breaking von...     

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.     

The Schwarzschild black hole’s remnant via the Bohr-Sommerfeld quantization rule

A d-dimensional Schwarzschild black hole is quantized by the action variable and the Bohr-Sommerfeld quantization rule in this paper. We find that the spectra of the horizon area and the entropy are evenly spaced. The black hole mass is also quantized and it’s spectrum spacing is proportional inversely to the mass. The ground state appears and has a constant entropy $\pi k_B$ . The ground state mass is shown to be the black hole remnant predicted by the generalized uncertainty principle and may be a candidate of dark matter.     

Green’s function for spinless particle via Parisi-Wu stochastic quantization method

An exact and analytic Green function for a spinless particle in interaction with an electromagnetic plane wave field, expressed in the coordinate gauge is given by Parisi-Wu stochastic quantization method. We separate the classical calculations from those related to the quantum fluctuation term. We have used a perturbative treatment relying on phase and configuration spaces formulation.Received: 27 January 2005, Revised: 3 April 2005, Published online: 8 June 2005PACS: 03.65.Ca, 03.65.Pm, 05.10.Gg     

A Generalization of the Stone–Von Neumann Theorem to Nonregular Representations of the CCR-Algebra

We give a classification, up to unitary equivalence, of the representations of the C*-algebra of the Canonical Commutation Relations which generalizes the classical Stone–von Neumann Theorem to the case of representations which are strongly measurable, but not necessarily strongly continuous. The classification includes all the (nonregular) representations which have been considered in physical models.     

Equivalence principle,the general theory of relativity,ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with valve properties -a one-way exchange of information—contradicts the equivalence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–15, January, 1984.     

Levi–Civita effect in the polarizable vacuum (PV) representation of general relativity

The polarizable vacuum (PV) representation of general relativity (GR), derived from a model by Dicke and related to the TH formalism used in comparative studies of gravitational theories, provides for a compact derivation of the Levi–Civita effect (both magnetic and electric), herein demonstrated.This revised version was published online in April 2005. The publishing date was inserted.