Einstein Gravitation Research Articles

Wormhole Restrictions from Quantum Energy Inequalities

Wormhole solutions, bridges that connect different parts of spacetime, were proposed early in the history of General Relativity. Soon after, it was shown that all wormholes violate classical energy conditions, which are non-negativity constraints on contractions of the stress–energy tensor. Since these conditions are violated by quantum fields, it was believed that wormholes can be constructed in the context of semiclassical gravity. But negative energies in quantum field theory are not without restriction: quantum energy inequalities (QEIs) control renormalized negative energies averaged over a geodesic. Thus, QEIs provide restrictions on the construction of wormholes. This work is a review of the relevant literature, thus focusing on results where QEIs restrict traversable wormholes. Both ‘short’ and ‘long’ (without causality violations) wormhole solutions in the context of semiclassical gravity are examined. A new result is presented on constraints on the Maldacena, Milekhin, and Popov ‘long’ wormhole from the recently derived doubled smeared null energy condition.

Kaluza–Klein Universe interacting with wet dark fluid in f(R,T) gravity

In this paper, we study the essence of [Formula: see text] gravitation theory in five-dimensional Universe and see the role of dark energy in the form of wet dark fluid in a Kaluza–Klein Universe. It is found that the dark energy is not exaggerated in contributing to the accelerating expansion of the Universe though the expansion is inherent as a result of the theory itself and due to the geometric contribution of matter. It is interesting to see that in some model it is found that there was some era before the beginning of the present era. Some of the models are seen to go to [Formula: see text]CDM models in late future as in Einstein gravitation theory, starting the evolution with a big bang. Most of the models undergo early inflation as well as late-time accelerating expansion thus defining as good models for real astrophysical situations, with dark energy playing fundamental role in these Universe. Most interesting observation from this investigation is that we can developed new isotropic and anisotropic models of Kaluza–Klein Universe.

A new unified model of dark matter and dark energy in 5-dimensional f(R,ϕ) gravity

We propose a new unified model that describes dark energy and dark matter in the context of [Formula: see text] gravity using a massive scalar field in five dimensions. The scalar field is considered in the bulk that surrounds the 3-brane in branworld model. We show that for a specific choice of the [Formula: see text] function, we can describe the Einstein gravitation in 4-dimensional space-time. We obtain a relationship between the speed of the Universe’s expansion and the speed of the bulk’s expansion. We also propose that the dark matter is represented by the scalar field mass and that the dark energy is a kinetic energy of this field. Finally, we show that, according to conditions, one can obtain the percentages of density of dark matter and the density of ordinary matter.

On the metrizability of the affine connectivity space and the unified theory of fundamental interactions

We propose the background connectivity interpret as the empirical connectivity, received as the particular case of the transition operator, which had been by induced by the collision integral. Approximating the transition operator by the differential operator we shall demand minimum variance of the given operator from the transition operator for the definition of the metric tensor. As a result we receive with the help of the variation formalism the differential equation of the regression, solving of which can find the metric tensor. By the help of the given tensor we receive the Christoffel symbols. Using the metric tensor and the Christoffel symbols can construct both the Einstein gravitation theory and the Chernikov gravitation theory with the two connectivity’s. Constructing the empirical connectivity theory we shall use the generalized functions, that implies the change of the space-time topology.

The dynamics of collaboration networks and the history of general relativity, 1925\u20131970

This paper presents a novel methodology for defining and analyzing the dynamics of the collaboration networks of scientists working on general relativity from the mid-1920s–1970. During these four and a half decades the status of the theory underwent a radical transformation: from a marginal theory before the mid-1950s to a pillar of modern physics. To investigate this passage—known as the renaissance of general relativity—we used a definition of collaboration networks broader than the co-authorship relations retrievable from online datasets. We constructed a multilayer network, in which each layer represents a different kind of collaboration. After having analyzed the evolution over time of specific parameters of the co-authorship network, we investigated the effects of adding one type of collaboration edge at a time, in a cumulative fashion, on the values of these parameters and on the topology of the collaboration network through time, including rapid shifts in the dynamic evolution of the largest component. This analysis provides robust quantitative evidence that a shift in the structure of the relativity collaboration network occurred between the late 1950s and the early 1960s, when a giant component started forming. We interpret this shift as the central social dynamic of the renaissance process and then identify its central actors. Our analysis disproves common explanations of the renaissance process. It shows that this phenomenon was not a consequence of astrophysical discoveries in the 1960s, nor was it a simple by-product of socio-economic transformations in the physics landscape after World War II.

The principle of equivalence as a criterion of identity

In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space–time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained.

There Is No Conspiracy of Inertia

I examine two claims that arise in Brown’s account of inertial motion in Physical Relativity (2005). Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that, while the theorems that motivate Brown’s second claim can be said to figure in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion.

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.

Einstein׳s physical strategy, energy conservation, symmetries, and stability: “But Grossmann & I believed that the conservation laws were not satisfied”

Recent work on the history of General Relativity by Renn et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein׳s physical strategy and the particle physics derivations compare? What energy–momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911–1914) of the canonical energy–momentum tensor and its translation-induced conservation? After initially using energy–momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance xμ′=Mνμxν to relate it to the canonical tensor. Usually he avoided using matter Euler–Lagrange equations and so was not well positioned to use or reinvent the Herglotz–Mie–Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor׳s asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell׳s theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). Einstein׳s theory thus has a symmetric canonical energy–momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom (later called “ghosts” in particle physics). Thus the Entwurf theory fails a 1920s–1930s a priori particle physics stability test with antecedents in Lagrange׳s and Dirichlet׳s stability work; one might anticipate possible gravitational instability.This critique of the Entwurf theory can be compared with Einstein׳s 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury׳s perihelion right. One can live with absolute rotation but cannot live with instability.Particle physics also can be useful in the historiography of gravity and space–time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether׳s work, sheds light on particle physics.

Towards the theory of regular accelerating Universe in Riemann-Cartan space-time

The problems of modern cosmology and attempts of its solution are considered. The applying of gravitation theory in the Riemann-Cartan space-time as the most natural generalization of Einstein gravitation theory in order to solve the principal cosmological problems is discussed. The gravitation theory in the Riemann-Cartan space-time leading to the solution of the problem of cosmological singularity and dark energy problem is analyzed.

Planck Quantization of Newton and Einstein Gravitation

In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight; for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale; for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.

Einstein's gravitation is Einstein-Grossmann's equations

While the philosophers of science discuss the General Relativity, the mathematical physicists do not question it. Therefore, there is a conflict. From the theoretical point view “the question of precisely what Einstein discovered remains unanswered, for we have no consensus over the exact nature of the theory's foundations. Is this the theory that extends the relativity of motion from inertial motion to accelerated motion, as Einstein contended? Or is it just a theory that treats gravitation geometrically in the spacetime setting?”. “The voices of dissent proclaim that Einstein was mistaken over the fundamental ideas of his own theory and that their basic principles are simply incompatible with this theory. Many newer texts make no mention of the principles Einstein listed as fundamental to his theory; they appear as neither axiom nor theorem. At best, they are recalled as ideas of purely historical importance in the theory's formation. The very name General Relativity is now routinely condemned as a misnomer and its use often zealously avoided in favour of, say, Einstein's theory of gravitation What has complicated an easy resolution of the debate are the alterations of Einstein's own position on the foundations of his theory”, (Norton, 1993) [1]. Of other hand from the mathematical point view the “General Relativity had been formulated as a messy set of partial differential equations in a single coordinate system. People were so pleased when they found a solution that they didn't care that it probably had no physical significance” (Hawking and Penrose, 1996) [2]. So, during a time, the declaration of quantum theorists: “I take the positivist viewpoint that a physical theory is just a mathematical model and that it is meaningless to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation.” (Hawking and Penrose, 1996) [2] seemed to solve the problem, but recently achieved with the help of the tightly and collectively synchronized clocks in orbit frontally contradicts fundamental assumptions of the theory of Relativity. These observations are in disagree from predictions of the theory of Relativity. (Hatch, 2004a, 2004b, 2007) [3,4,5]. The mathematical model was developed first by Grossmann who presented it, in 1913, as the mathematical part of the Entwurf theory, still referred to a curved Minkowski spacetime. Einstein completed the mathematical model, in 1915, formulated for Riemann´s spacetimes. In this paper, we present as of General Relativity currently remains only the mathematical model, darkened with the results of Hatch and, course, we conclude that a Einstein´s gravity theory does not exist.

Friedman׳s thesis

This essay examines Friedman׳s recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman׳s characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman׳s thesis is defensible.

Rudiments of IsoGravitation for Matter and its IsoDual for AntiMatter

In this paper, we hope to initiate due scientific process on some of the historical criticisms of Einstein gravitation expressed by Einstein himself as well as by others. These criticisms have remained widely ignored for one century and deal with issues such as: the apparent lack of actual, physical curvature of space due to the refraction of star-light within the Sun chromosphere; the absence of a source in the field equations due to the electromagnetic origin (rather than the charge) of gravitational masses; the lack of clear compatibility of general relativity with special relativity, interior gravitational problems, electrodynamics, quantum mechanics and grand unifications; the lack of preservation over time of numerical predictions inherent in the notion of covariance; and other basic issues. We show that a resolution of these historical doubts can be apparently achieved via the use of the novel isomathematics and related iso-Minkowskian geometry based on the embedding of gravitation in generalized isounits, with isodual images for antimatter. Thanks to half a century of prior research, we then show that the resulting new theory of gravitation, known as isogravitation, preserves indeed Einstein's historical field equations although formulated on the iso-Minkowskian geometry over isofields whose primary feature is to have null isocurvature. We then show that isogravitation allows: Einstein field equations to achieve a unified treatment of generally inhomogeneous and anisotropic, exterior and interior gravitational problems; the achievement of a clear compatibility with 20th century sciences; the achievement of time invariant numerical predictions thanks to the strict invariance (rather than covariance) of gravitation under the Lorentz-Santilli isosymmetry; the apparent achievement of a consistent representation of the gravitational field of antimatter thanks ti the isodual iso-Minkowskian geometry; the apparent achievement of a grand unification inclusive of electroweak and gravitational interactions for matter and antimatter without known causality or structural inconsistencies; and other advances. We then present, apparently for the first time, the isogravitational isoaxioms characterized by the infinite family of isotopies of special relativity axioms as uniquely characterized by the Lorentz-Santilli isosymmetry which are applicable to both exterior and interior isogravitational problems of matter with their isodual for antimatter. We finally show, also for the first time, the apparent compatibility of isogravitation with current knowledge on the equivalence principle, matter black holes and other gravitational data.

Diffeomorphism-invariant lattice actions

We present a lattice-discretization procedure which is based on the simplicial lattice preserves diffeomorphism invariance. The presented procedure is the straightforward generalization for the procedure used for discretization of the spinor gravity [7]. As a stable way to guarantee the removing of the lattice regularization, i.e. the continuum limit, for lattice diffeomorphism invariant theories, we propose to tune the system to point of the phase transition. We expect that the Einstein gravitation is achieved at this point.

THE RELATION BETWEEN THE MODEL OF A CRYSTAL WITH DEFECTS AND PLEBANSKI'S THEORY OF GRAVITY

In the present investigation, we show that there exists a close analogy of geometry of space–time in general relativity (GR) with a structure of defects in a crystal. We present the relation between the Kleinert's model of a crystal with defects and Plebanski's theory of gravity. We have considered the translational defects — dislocations and the rotational defects — disclinations — in the three- and four-dimensional crystals. The four-dimensional crystalline defects present the Riemann–Cartan space–time which has an additional geometric property — "torsion" — connected with dislocations. The world crystal is a model for the gravitation which has a new type of gauge symmetry: the Einstein's gravitation has a zero torsion as a special gauge, while a zero connection is another equivalent gauge with nonzero torsion which corresponds to the Einstein's theory of "teleparallelism". Any intermediate choice of the gauge with nonzero connection [Formula: see text] is also allowed. In the present investigation, we show that in the Plebanski formulation the phase of gravity with torsion is equivalent to the ordinary or topological gravity, and we can exclude a torsion as a separate dynamical variable.

Harmonic and Wave Maps Coupled with Einstein’s Gravitation

In this paper we discuss the coupled dynamics, following from a suitable Lagrangian, of a harmonic or wave map $\phi$ and Einstein's gravitation described by a metric $g$. The main results concern energy conditions for wave maps, harmonic maps from warped product manifolds, and wave maps from wave-like Lorentzian manifolds.

Phase transitions in spinor quantum gravity on a lattice

We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is suitable for describing large nonperturbative and fast-varying fluctuations of metrics. Although the quantum curved space turns out to be on the average flat and smooth owing to the non-compressibility of the fundamental fermions, the low-energy Einstein limit is not automatic: one needs to ensure that composite metrics fluctuations propagate to long distances as compared to the lattice spacing. One way to guarantee this is to stay at a phase transition. We develop a lattice mean field method and find that the theory typically has several phases in the space of the dimensionless coupling constants, separated by the second order phase transition surface. For example, there is a phase with a spontaneous breaking of chiral symmetry. The effective low-energy Lagrangian for the ensuing Goldstone field is explicitly diffeomorphism-invariant. We expect that the Einstein gravitation is achieved at the phase transition. A bonus is that the cosmological constant is probably automatically zero.

Spinor-unit field representation of electromagnetism applied to a model inflationary cosmology

The new spinor-unit field representation of the electromagnetism \cite{Nash2010} (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early universe. The solution of the coupled Euler-Lagrange field equations yields a scale factor $a(t)$ (comoving coordinates) that initially exponentially increases $N$ e-folds from $a(0) \approx 0$ to $a_{1} = a(0) {e}^{N} $ ($N$ = 60 is illustrated), then exponentially decreases, then exponentially increases to $a_{1}$, and so on almost periodically. (Oscillatory cosmological models are not knew, and have been derived from string theory and loop quantum gravity.) It is not known if the scale factor escapes this periodic trap. This model is noteworthy in several respects: $\{1\}$ All fundamental fields other than gravity are realized by spinor fields. $\{2\}$ A plausible connection between the \emph{unit} field $\mathbf{u}$ and the generalization of the photon wave function with a form of Dark Energy is described, and a simple natural scenario is outlined that allocates a fraction of the total energy of the Universe to this form of Dark Energy. $\{3\}$ A solution of an analog of the pure Einstein-Maxwell equations is found. This approach is in contrast with the method followed to obtain a solution of the well known Friedmann model of a radiation-dominated universe.

Erratum to: Local axioms in disguise: Hilbert on Minkowski diagrams

During the production of the article, some errors and misprints have been overlooked. The author only noticed them after the paper was already online. On page 7 of the online version, lines 14–17, the last sentence of the quote from Hilbert should read: “In this same way, electromagnetic inertia and Einsteinian gravitation, [as conceived] with the corresponding concepts of the classical theories, are compatible [vertraglich], inasmuch as these classical concepts can be conceived as limiting cases of the more general concepts in the new theories.” Page 9, line 14 should read: “an axiom system having all the known facts of a given scientific domain represented as deducible from the axioms ...”. Page 16, line 9 should read: “Furthermore, one may ask ...”. Page 17, line 6 should read: “he took primitive evidence to be akin to proto-arithmetical-algebraical evidence”. Page 18, line 4 should read: “certain questions are formulated, to which geometrical intuition contributes”. Pages 27, 28 and 30, one should read: “discriminant” instead of “determinant” with regard to binary quadratic forms. Although terminology is not unanimously settled on this score and varies from one author to another, consistent choices should be made in the paper when talking about Lagrange’s reduction algorithm on the one hand and Hermite-Minkowski’s setting on the other hand. Therefore on page 27, lines 12, 17 and