Einstein 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.

The (Elusive) Theory of Everything

Stephen Hawking's work on black holes and the origin of the universe is arguably the most concrete progress theoretical physicists have made toward reconciling Einstein's gravitation and quantum physics into one final theory of everything. Physicists have a favorite candidate for such a theory, string theory, but it comes in five different formulations, each covering a restricted range of situations. A network of mathematical connections, however, links the different string theories into one overarching system, enigmatically called M-theory: perhaps the network is itself the final theory. In a new book, The Grand Design, Hawking and Caltech physicist Leonard Mlodinow argue that the quest to discover a final theory may in fact never lead to a unique set of equations. Every scientific theory, they write, comes with its own model of reality, and it may not make sense to talk of what reality actually is. This essay is based on that book.

REPULSIVE CASIMIR FORCES AND ALTERNATIVES TO EINSTEINIAN GRAVITY

A basic property of the Casimir force is that, in most cases, it is attractive. The quest for workable configurations which exhibit repulsion is, at the same time, important and difficult, both in the nanophysics laboratory (e.g. to avoid stickness) and at cosmological scales (to account for the accelerated expansion of our universe). We shall here report on some configurations which exhibit the two signs of the Casimir force in function of the distance, and also on some alternatives to Einsteinian gravitation with the eventual aim to try to get around the cosmological constant problem.

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.

MASS SPECTRUM OF QUANTUM BLACK HOLES FROM NEWTONIAN-GRAVITY AND QUANTUM-POTENTIAL APPROACH

In earlier papers, we have introduced an approach for quantum-gravitational bodies based on the quantum potential written in the form of an equation of state to be added to equations of gravitation theories. In the case of Einsteinian gravitation, we have obtained quantum black holes by rough calculation but, in the case of Newtonian gravitation, with additional assumption on "no-escape" radius for light, the same bodies may be obtained by simple but rigorous mathematical calculation. This paper deals with Newtonian rotating quantum black holes and derives their mass spectrum that is closed to those of some authors based on relativistic treatment.

Further Clarification of “New Einstein Gravitation”

Further Clarification of “New Einstein Gravitation”

The Pythagorean Theorem: What Is It About?

(2006). The Pythagorean Theorem: What Is It About? The American Mathematical Monthly: Vol. 113, No. 3, pp. 261-265.

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.

General Relativity in the English-speaking World: The Contributions of Henry L. Brose

The story of how the theory of general relativity found its way into the English speaking world during the Great War has often been told: it is dominated by the towering figure of the Cambridge astronomer Arthur Stanley Eddington, who (in 1916, and through the good services of the Dutch physicist Willem de Sitter) received copies of the papers Einstein had presented to the Berlin Academy in 1915. Eddington engaged in promoting the new theory, and in order to put one of its predictions — the bending of light in a gravitational field — to the test, he arranged for the famous expeditions to observe the eclipse of 29 May 1919 to be mounted, the results of which, presented in November of the same year, were the major breakthrough of general relativity and provoked a public interest unprecedented in the whole history of science. But a history of general relativity in the English-speaking world would be thoroughly incomplete if it did not take into account the contributions made by another, nowadays almost forgotten but at that time probably the most prolific and most dedicated of its popularizers, the Australian physicist and translator Henry L. Brose. Largely overlooked in recent accounts of the history of general relativity, Brose's rendering into English of a series of excellent German works on the theory was decisive for its understanding in the Anglo-Saxon world. The texts he chose (including Moritz Schlick's Space and Time in Contemporary Physics and Hermann Weyl's Space, Time, Matter) were among the first and most important that had so far appeared on the subject, and their English translations were published at a time when accounts of what was to be called 'one of the greatest of achievements in the history of human thought' were scarce and badly needed in Britain. Also, it will become clear from a closer look at both Brose's biography and the tense political situation between Britain and Germany shortly after the Great War, that hardly any of those works would have made its way into England so promptly (if at all) if not for Brose's enormous personal efforts and dedication. This paper retraces Brose's role as a translator and promotor of general relativity in its early days, thus shedding light on the mechanisms of knowledge transfer during and after the First World War.

GRAVITY TESTS IN THE SOLAR SYSTEM AND THE PIONEER ANOMALY

We build up a new phenomenological framework associated with a minimal generalization of Einsteinian gravitation theory. When linearity, stationarity and isotropy are assumed, tests in the solar system are characterized by two potentials which generalize respectively the Newton potential and the parameter γ of parametrized post-Newtonian formalism. The new framework has the capability to account for the Pioneer anomaly while preserving the compatibility of other gravity tests with general relativity.

New Hamiltonian formalism and quasilocal conservation equations of general relativity

I describe the Einstein's gravitation of $3+1$ dimensional spacetimes using the (2,2) formalism without assuming isometries. In this formalism, quasilocal energy, linear momentum, and angular momentum are identified from the four Einstein's equations of the divergence-type, and are expressed geometrically in terms of the area of a two-surface and a pair of null vector fields on that surface. The associated quasilocal balance equations are spelled out, and the corresponding fluxes are found to assume the canonical form of energy-momentum-flux as in standard field theories. The remaining non-divergence-type Einstein's equations turn out to be the Hamilton's equations of motion, which are derivable from the nonvanishing Hamiltonian by the variational principle. The Hamilton's equations are the evolution equations along the out-going null geodesic whose affine parameter serves as the time function. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasilocal quantities reduce to the Bondi energy, linear momentum, and angular momentum, and the corresponding fluxes become the Bondi fluxes. The quasilocal angular momentum turns out to be zero for any two-surface in the flat Minkowski spacetime. I also present a candidate for quasilocal rotational energy which agrees with the Carter's constant in the asymptotic region of the Kerr spacetime. Finally, a simple relation between energy-flux and angular momentum-flux of a generic gravitational radiation is discussed, whose existence reflects the fact that energy-flux always accompanies angular momentum-flux unless the flux is an $s$-wave.

Nonstationary Cosmological Models with Rotation

Two nonstationary cosmological models with rotation are constructed for the Bianchi II metric within the Einstein gravitation theory. The first model is filled with a co-moving perfect liquid and radiation field and is characterized by nonzero expansion, rotation, and acceleration. A perfect liquid which is not co-moving with a reference system is a source of gravitation for the second model. The second model corresponds to nonzero rotations and accelerations.

Gauged harmonic maps, Born‐Infeld electromagnetism, and magnetic vortices

AbstractWe study maps from a 2‐surface into the standard 2‐sphere coupled with Born‐Infeld geometric electromagnetism through an Abelian gauge field. Such a formalism extends the classical harmonic map model, known as the σ‐model, governing the spin vector orientation in a ferromagnet allows us to obtain the coexistence of vortices and antivortices characterized by opposite, self‐excited, magnetic flux lines. We show that the Born‐Infeld free parameter may be used to achieve arbitrarily high local concentration of magnetic flux lines that the total minimum energy is an additive function of these quantized flux lines realized as the numbers of vortices antivortices. In the case where the underlying surface, or the domain, is compact, we obtain a necessary sufficient condition for the existence of a unique solution representing a prescribed distribution of vortices antivortices. In the case where the domain is the full plane, we prove the existence of a unique solution representing an arbitrary distribution of vortices and antivortices. Furthermore, we also consider the Einstein gravitation induced by these vortices, known as cosmic strings, establish the existence of a solution representing a prescribed distribution of cosmic strings cosmic antistrings under a necessary sufficient condition that makes the underlying surface a complete surface with respect to the induced gravitational metric. © 2003 Wiley Periodicals, Inc.

Letter: Axisymmetric Vacuum Gravitation in Canonical Coordinates

In canonical coordinates, one can specify the axisymmetric solutions of Einstein's vacuum gravitation equations by assigning a generating function a(t, z) that prescribes the light speed along the axis of symmetry. To assist in the identification of those axial generators that will produce the different asymptotically flat space-times, we now examine what coordinate freedom persists in the metric, and link this to our earlier investigation of similarity solutions.

Experimental tests of relativistic gravity

The confrontation between Einstein's gravitation theory and experimental results, notably binary pulsar data, is summarized and its significance discussed. Experiment and theory agree at the 10 −3 level or better. All the basic structures of Einstein's theory (coupling of gravity to matter; propagation and self-interaction of the gravitational field, including in strong-field conditions) have been verified. However, the theoretical possibility that scalar couplings be naturally driven toward zero by the cosmological expansion suggests that the present agreement between Einstein's theory and experiment might be compatible with the existence of a long-range scalar contribution to gravity (such as the dilaton field, or a moduli field, of string theory). This provides a new theoretical paradigm, and new motivations for improving the experimental tests of gravity.

A Polyakov fermionic string as a quantum state of Einstein theory of gravitation

We show that a Polyakov fermionic string functional integral in the presence of the external spatial Ashtekar-Sen connection solves the Wheeler-De Witt equation of Einstein gravitation theory written in terms of the Ashtekar-Sen variables.

Nonsingular Metric Elastic Universe

In the RTFD(Gusev (1986)) the conception of a Sakharov - Wheeler Metric Elasticity(SWME)(Sakharov (1967), Wheeler (1970)) had been worked out. On the basis of the exact solutions of Einstein equations and qualitative analysis RTFD the global evolution have been studied and the phase portraits of the early Universe is being constructed. An analysis of phase portraits show on the possibility description of spontaneous creation of Universe from an initial Minkowskian's vacuum to an inflationary de Sitter space-time in the frame of phenomenological non-quantum theory (Guth (1991)). During the past decade, a radically new picture of cosmology has emerged. The present homogeneous expanding Universe would have stated out with a de Sitter phase. The purpose of this paper is to shown that the geometry-dynamical approach to the Einstein's gravitation theory in the frame RTFD also is leaded to the nonsingular cosmological models (Brandenberger (1993)). Let us to propose that before the some moment of time the Universe is at the vacuum state and is described the geometry of Minkowskian's space. Deformations of vacuum state, identifying with empty Mikowskian's space are described by the deformations tensor, An arising of deformation ∊αβis leaded to appearance of the stress tensor ∊αβand the energy-momentumTαβ(∊γδ) which is connected with “creating” particles in the Universe. Here we are considered the deformations of Minkowskian's space (the initial vacuum state with∞αβ = 0) at the linear theory (~ ∊) of finite deformations. The final deformation stategαβare searched in the metric class of Friedmann's cosmological spaces. In the comoving reference systemUα(0, 0, 0, 1) the Friedmann's equations have form (Narlikar & Padmanabhan (1983), and Gusev (1989)):where R(t) is so called the expansion factor at the Robertson - Walker line element, k is the curvature parameter with the possible values −1, 0, + 1, P is pressure,k1,k2are the some combination from a Lame coefficients,l02is a “initial radius” Universe, a free parameter model. The phase space of this model is the two-dimensional (R,Ṙ) plane. We note that there is only two singular points (Ṙ= 0,Ṙ= 0) in the phase plane. The one of those points isR=l0,Ṙ= 0 and corresponds to Minkowski space - time. There are two classes trajectories which are asymptotically de Sitter. Those starting at large positive values ofṘgo off toṘ= + ∞, reaching their asymptotic value of H from above. Those starting with large negative values ofṘtend toR= + ∞ withṘ> 0. For small values ofṘand R we can see that there are periodic solutions about Minkowski space. The corresponding solutions oscillate with frequency given byH0(which is possible equal planck scale) about Minkowski space. Based on the preceding discussion of asymptotic solutions we see that there is a separatrix (Gusev, (1989)) in phase space dividing solutions which tend toR= + ∞ from those which oscillate or tend toR=l0. The above analyses of the phase portraits is an indication that in our theory Minkowski space may be unstable toward homogeneous deformations. We stress that all the general features of the phase portrait analyses are true for quadratic deformations of gravitational vacuum. Our model incorporates a very important feature: in the asymptotic de Sitter region, the quadratic deformations and temperature effects does not have an important effect on the geometry. The effective gravitational constant of coupling goes to zero as space - time approaches de Sitter space. In this sense the model is asymptotically free (gravitational confinement Linde, (1990)). At the late times the solutions are described a evolution of the de Sitter UniverseR~expHt(Hoyle et al. (1993)).

CPN-1 MODEL AS REDUCTION OF GRAVITY THEORIES

A complete series of the gauged CP N-1 nonlinear sigma models is obtained from the Einstein's gravitation by a reduction mechanism, assuming the SU (N) symmetry as the isometry of the metric. Some physical implications of this result are discussed briefly.

Massive Yang-Mills Field Theory with Conformal (Weyl) Invariance

A massive Yang-Mills field theory with the conformal (Weyl) invariance and gauge invariance is proposed. It involves the gravitational and various gauge interactions, in which all the mass terms appear as the uniform interactional form . When the conformal and gauge symmetries are broken spontaneously, the Einstein gravitation emerges and all the fields obtain masses, this theory is renormalizable and unitary with the gravitation ignored. Finally we give a relation between the theory and the Higgs mechanism.

Einstein and the History of General Relativity. Don Howard , John Stachel

<i>Einstein and the History of General Relativity</i>. Don Howard , John Stachel