Einstein's Theory Of Gravitation Research Articles

Einstein's ‘Zürich Notebook’ and his journey to general relativity

On the basis of his ‘Zürich Notebook’ I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main physical arguments and conceptual difficulties that delayed his discovery of general relativity by about three years. Together with the ‘Entwurf’ theory in collaboration with Marcel Grossmann, these notes also show that the final theory was missed late in 1912 within a hair's breadth. The Einstein-Grossmann theory, published almost exactly hundred years ago, contains, however, virtually all essential elements of Einstein's definite gravitation theory.

AREA SPECTRUM OF THE EXTREME REISSNER–NORDSTRÖM BLACK HOLE

Motivated by the new interpretation on quasinormal modes by Maggiore, we investigate the quantization of the extreme Reissner–Nordström black hole in the four-dimensional spacetime. Following Kunstatter's method, we derive the equally spaced area spectrum and the entropy, however the spacing differs from Setare's result via Hod's proposal. Moreover, our result is in full agreement with Bekenstein's result as well as the claim that black hole's area is equidistant in Einstein's Gravity theory by Wei et al.

Second-order phase transition of Kehagias–Sfetsos black hole in deformed Hořava–Lifshitz gravity

We study the second-order phase transition (SOPT) for the spherically symmetric Kehagias–Sfetsos (KS) black hole in the deformed Hořava–Lifshitz gravity by applying the methods of equilibrium and non-equilibrium fluctuations. We find that, although the KS black hole has only one mass parameter as the usual Schwarzschild ones, the SOPT will take place if the mass of the KS black hole changes across the critical point 5+33(33−1)16ω. The result show us that there is difference between the Hořava–Lifshitz gravity and the Einstein's gravity theory.

SL(2,C)gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.

TWO-CONNECTION RENORMALIZATION AND NON-HOLONOMIC GAUGE MODELS OF EINSTEIN GRAVITY

A new framework for perturbative quantum gravity is proposed following the geometry of non-holonomic distributions on (pseudo)Riemannian manifolds. There are considered such distributions and adap-ted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two-loop renormalizable effective actions. We use a key result from our partner work arXiv: 0902.0911 that the classical Einstein gravity theory can be reformulated equivalently as a non-holonomic gauge model in the bundle of affine/de Sitter frames on pseudo-Riemannian space–time. It is proven that (for a class of non-holonomic constraints and splitting of the Levi–Civita connection into a "renormalizable" distinguished connection, on a base background manifold, and a gauge-like distortion tensor, in total space) a non-holonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one- and two-loop levels and renormalization group equations for non-holonomic configurations.

NONHOLONOMIC DISTRIBUTIONS AND GAUGE MODELS OF EINSTEIN GRAVITY

For (2 + 2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi–Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric tensor. Reformulation of the Einstein equations in nonholonomic variables (tetrads and new connections, for instance, with constant coefficient curvatures and/or Yang–Mills like potentials) reveals hidden geometric and rich quantum structures. It is shown how the Einstein gravity theory can be redefined equivalently as certain gauge models on nonholonomic affine and/or de Sitter frame bundles. We speculate on possible applications of the geometry of nonholonomic distributions with associated nonlinear connections in classical and quantum gravity.

INTEGRATION OVER CONNECTIONS IN THE DISCRETIZED GRAVITATIONAL FUNCTIONAL INTEGRALS

The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some directions. This point is studied in the case of the discrete form of the first-order formulation of the Einstein gravity theory. Here the result of interest can be defined as generalized function (of the rest of variables of the type of tetrad or elementary areas), i.e. a functional on a set of probe functions. To define this functional, we calculate its values on the products of components of the area tensors, the so-called moments. The resulting distribution (in fact, probability distribution) has singular (δ-function-like) part with support in the nonphysical region of the complex plane of area tensors and regular part (usual function) which decays exponentially at large areas. As we discuss, this also provides suppression of large edge lengths which is important for internal consistency, if one asks whether gravity on short distances can be discrete. Some other features of the obtained probability distribution including occurrence of the local maxima at a number of the approximately equidistant values of area are also considered.

BRANES AND QUANTIZATION FOR AN A-MODEL COMPLEXIFICATION OF EINSTEIN GRAVITY IN ALMOST KÄHLER VARIABLES

The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, [Formula: see text] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metric g on a manifold V enabled with a necessary type nonholonomic 2 + 2 distribution. Such nonholonomic symplectic variables allow us to formulate the problem of quantizing Einstein gravity in terms of the A-model complexification of almost complex structures on V, generalizing the Gukov–Witten method [1]. Quantizing [Formula: see text], we derive a Hilbert space as a space of strings with two A-branes which for the Einstein gravity theory are nonholonomic because of induced nonlinear connection structures. Finally, we speculate on relation of such a method of quantization to curve flows and solitonic hierarchies defined by Einstein metrics on (pseudo) Riemannian spacetimes.

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

We argue that the Einstein gravity theory can be reformulated in almost Kahler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation (NGT) on manifolds enabled with nonholonomic distributions is analyzed. There are considered some conditions when the fundamental geometric and physical objects are determined/ modified by nonholonomic deformations in general relativity or by contributions from Ricci flow theory and/or quantum gravity. We prove that in such NGT, for certain classes of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic NGT models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in NGT. Finally we conclude that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of certain models and/or classes of unconstrained solutions.

Nash Bosonization in Path Integral for Quantum Riemannian Geometry

We propose an effective quantum theory for Einstein Gravitation theory by making use of the Nash Theorem of Riemann Metrics parametrized by immersions. We show the usefulness of this phenomenological (low energy) path integral bosonization scheme through the evaluation for the Classical Newton potential by means of a Wilson loop path integral evaluation.

Generalized Vaidya spacetime in Lovelock gravity and thermodynamics on the apparent horizon

We present a kind of generalized Vaidya solutions in a generic Lovelock gravity. This solution generalizes the simple case in Gauss-Bonnet gravity reported recently by some authors. We study the thermodynamics of apparent horizon in this generalized Vaidya spacetime. Treating those terms except for the Einstein tensor as an effective energy-momentum tensor in the gravitational field equations, and using the unified first law in Einstein gravity theory, we obtain an entropy expression for the apparent horizon. We also obtain an energy expression of this spacetime, which coincides with the generalized Misner-Sharp energy proposed by Maeda and Nozawa in Lovelock gravity.

Evolution of density perturbations in double exponential quintessence models

In this work we investigate the evolution of matter (linear) density perturbations for quintessence models with a self-interaction potential that is a combination of exponentials. One of the models is based on the Einstein theory of gravity, while the other is based on the Brans-Dicke scalar tensor theory. We constrained the parameter space of the models by using the determinations of the growth rate of perturbations derived from data of the 2-degree Field Galaxy Redshift Survey.

GLUEBALL MASSES FROM ADS6 GRAVITY THEORY

In view of the general holographic principle between gauge theories and gravity, We calculate the mass spectra of several typical QCD4 glueballs in term of AdS 6 AdS -Schwarzschild black hole metric of Einstein gravity theory. The obtained mass spectra are numerically in consistent with those from the AdS 7 × S 4 black hole metric of the 11-dimensional supergravity. Besides, by separating the thermal circle from the extra dimensions, we find a novel exact D p-brane solution of Type IIB supergravity, which might provide a scenario for studying the non-perturbative dynamics of QCD4 from the perspective of Type IIB supergravity.

A CLASS OF NONLINEAR RELATIVISTIC MODELS FOR NUCLEAR MATTER AND THE BINARY PULSAR J0737-3039A

In this work, we calculate the moment of inertia of the pulsar of the binary system J0737-3039A in the framework of Einstein's gravitational theory combined with a relativistic field theoretical approach for nuclear matter in the slow rotating regime, taking into account that the star's frequency is much smaller than Kepler's frequency. In the description of the EoS for nuclear matter, we consider a generalized class of relativistic multi-baryon Lagrangian density mean field approach which contains adjustable nonlinear couplings of the meson fields with the baryon fields. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we determine the EoS of the pulsars. By analyzing the results, dynamical constraints for neutron star models are identified.

False vacuum bubble nucleation due to a nonminimally coupled scalar field

We study the possibility of forming the false vacuum bubble nucleated within the true vacuum background via the true-to-false vacuum phase transition in curved spacetime. We consider a semiclassical Euclidean bubble in the Einstein theory of gravity with a nonminimally coupled scalar field. In this paper we present the numerical computations as well as the approximate analytical computations. We mention the evolution of the false vacuum bubble after nucleation.

Accelerating Hilbert–Einstein universe without dynamic dark energy

By using an unmodified Einstein gravity theory it is shown that all of the speeding-up effects taking place in the current universe are entirely due to the quantum effects associated with the background radiation or to the combination of such effects with those derived from the presence of a cosmological constant, without invoking any dynamic dark energy component. We obtain that in both cases the universe accelerates at a rate slightly beyond what is predicted by a cosmological constant but does not induce any big rip singularity in the finite future.

Different canonical formulations of Einstein’s theory of gravity

We describe the four most famous versions of the classical canonical formalism in the Einstein theory of gravity: the Arnovitt-Deser-Misner formalism, the Faddeev-Popov formalism, the tetrad formalism in the usual form, and the tetrad formalism in the form best suited for constructing the loop theory of gravity, which is now being developed. We present the canonical transformations relating these formalisms. The paper is written mainly for pedagogical purposes.

Post-Einsteinian tests of gravitation

Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy–momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation constant by two running couplings which depend on scale and differ in the two sectors of traceless and traced tensors. The metric and curvature tensors in the field of the Sun, which were obtained in previous papers within a linearized approximation, are then calculated without this restriction. Modifications of gravitational effects on geodesics are then studied, allowing one to explore phenomenological consequences of extensions lying in the vicinity of general relativity. Some of these extended theories are able to account for the Pioneer anomaly while remaining compatible with tests involving the motion of planets. The PPN ansatz corresponds to peculiar extensions of general relativity which do not have the ability to meet this compatibility challenge.

THE FATE OF THE FALSE VACUUM IN EINSTEIN GRAVITY THEORY WITH NONMINIMALLY-COUPLED SCALAR FIELD

The decay of false vacuum via the true vacuum bubble nucleation has been explored in Einstein theories of gravity with nonminimally-coupled scalar field using Coleman–De Luccia's semiclassical instanton approximation. In this case the false vacuum decay rates and the radius of the bubbles in Coleman's thin-wall approximation have been computed analytically and numerically with several values of nonminimal coupling constant and compared with the standard result obtained by Coleman–De Luccia in the context of scalar field minimally-coupled to Einstein gravity.

NEW GEOMETRIC FORMALISM FOR GRAVITY EQUATION IN EMPTY SPACE

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.