Einstein cartan theory as an averaged theory of gravity juliane behrend instituut voor theoretische fysica, universiteit utrecht, the netherlands. Einsteincartandirac gravity with u 1 symmetry breaking. Research article is einstein cartan theory coupled to. Cartan or einsteincartansciamakibble ecsk theory of. Kinematics of einsteincartan universes cambridge repository. Shortly after the year 2000, myron evans developed the einstein cartan evans theory ece theory 1, 2, 3 as a replacement, and was even able to unify this with electrodynamics and quantum mechanics.
Einsteincartan gravity in particle physics and cosmology nikodem j. Pdf there are various generalizations of einsteins theory of gravity gr. The beginning of metricallyaffine space manifold theory was marked by e. A completely equivalent gauge is the absence of cartan curvature. Like the gap field, the tap field is symmetric in its indices. Einsteincartanheisenberg theory of gravity with dynamical. He set up a theory of teleparallelism which explains gravity by a theory in. In the late 1950s, the theory of gravitation with spin and torsion was independently rediscovered by sciama and kibble. On the mathematics of coframe formalism and einstein. There are various generalizations of einsteins theory of gravity gr.
Derivation of the local lorentz gauge transformation of a dirac spinor field in quantum einstein cartan theory rainer w. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and bianchi identities, and eventually, we will end up with einstein cartan sciamakibble field equations and conservation laws in their implicit formulation. Institute of theoretical physics warsaw university 00. For the einstein cartan theory with the barberoimmirzi parameter this scheme was applied recently in 16, where the previous results for the oneloop divergences in the quantum gr with interacting fermion currents 17 have been used. Muschik it is shown, that the usually considered spin balances are too restrictive and only valid for pointlike particles. Geometry of spacetime einstein theory of gravity ii.
In hehls opinion einsteincartan theory is an even more beautiful theory than einsteins general relativity because of its relation to the poincare group. The general theory of relativity iowa state university. Keywords einstein cartan theory, cosmological model, anisotropy, galaxies and stellar bodies. Can torsion play a role in angular momentum conservation law. It has been described as the most beautiful of all the existing physical theories 1. Constitutive theory in general relativity and einstein cartan theory. The einstein cartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the density of intrinsic angular momentum. Constitutive theory in general relativity and einstein. The pure theory scale is l0 while potential deviation from the pure theory is represented by l. Indeed they may be considered as a conservation law for a certain sparling 3form defined on the bundle of orthonormal frames over spacetime. The einsteincartan theory is a modified theory of gravity, that is an.
Feb 18, 2011 einstein gr is dead, viva einsteincartan gravity. Relativistic kinematics in einsteincartan theory a theory is something nobody believes, except the person who made it. View the article pdf and any associated supplements and figures for a period of 48 hours. Einsteincartan theory introduction faculty of physics. As eulerlagrange equations of a lagrangian field theory, these einstein cartan equations lend themselves to many alternative kinematical descriptions. Geometric solution of the hierarchy problem by means of einstein cartan torsion carl f. In the present work we use the third possibility for the quantum einstein cartan theory. Poplawski department of mathematics and physics university of new haven west haven, ct, usa department of physics seminar indian institute of technology, hyderabad, india 2223 november 2016. Universe, black holes, and particles in spacetime with torsion. Could the theory of relativity actually have been conceived by the other einstein. It is certainly one of the most remarkable achievements of science to date, it was developed by einstein with little or no experimental motivation but driven instead by philosophical questions. The grand event was einsteins publication of his general theory of relativity in 1915. In einstein s theory of gravitation, mass directly influences the geometry but spin has no such dynamical effect. The di erence being that the gauge group of the former is the poincare group, while in the latter case one has gauge groups like su3 or su2.
Based on the fundamental insights of albert einstein and elie cartan, evans theory takes the geometry of spacetime itself as the origin of all forces of nature. Geometric solution of the hierarchy problem by means of. An experiment is something everybody believes, except the person who made it. Shapiro, new york times bestselling author of the art forger and the muralist this is a mustread. Einstein postulated the principles of special relativity 1906 to 1915. The einstein cartan theory ect of gravity is a modi. I in a riemann cartan spacetime the di erence between the. In the einsteincartan theory of torsionfree gravity coupling to massless fermions, the fourfermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the immirzi parameter. Einstein cartan theory is an extension of the standard formulation of general relativity where torsion the antisymmetric part of the affine connection is nonvanishing. New gauge symmetry in gravity and the evanescent role of. Cartan equations versus einstein equations in classical gravity. Enthusiasts may wish to delve deeper by inspecting the primary research papers which led to the new theory, einstein cartan evans theory or ece theory as it is also known. New gauge symmetry in gravity and the evanescent role of torsion. Or one could go via einstein maxwell dilaton theory emd by.
One peculiarity of einstein cartan theory is that the torsion. The reader is assumed to have but little mathematical knowledge. Huntsville, al 35899, usa i department of physics, university of michigan, ann arbor, mi 48109, usa received 6 june 1994 abstraft we consider selfconsistent spinning fluid cosmologies in. Cartans theory, however, was proposed before the discovery of. Twospinor differential form of einsteins equations. In einsteincartan theory, by the use of the general noether the orem, the general. The coupling between the spin of elementary particles and torsion in the einstein cartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin. The spacetime torsion is found to be given algebraically in terms of a quadratic spinor condensate field. What is the present status of the einsteincartan theory. Cartan theory with torsion over a principal fibre bundle.
Einstein cartan theory project gutenberg selfpublishing. A dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. Feb 19, 2017 einstein cartan theory is a variation of general relativity in which the affine connection is no longer presumed to be torsionfree. The evanss ece theory and the einsteins tetrad field. The einsteincartan theory ect of grav ity is a modification of general relativity the ory grt, allowing spacetime to have torsion, in addition to curvature. Einstein and hilbert extended the theory of special relativity to the theory of general relativity for gravitation. Albert einstein 5 preface december, 1916 the present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view. We see that the einstein connection is the gravitational analogue of the g field in. This work derives the elements of einsteincartan theory ec from. August, 1997 abstract the spintorsion sector of a new gaugetheoretic formulation of gravity is analysed and the relationship to the einsteincartankibble.
The phase structure of einsteincartan theory sciencedirect. The geometry of this continuum is curved and the amount of curvature in a region encodes the strength of the gravitational. Derivation of einsteincartan theory from general relativity arxiv. Tetrad currents in the einstein cartan theory we propose that the symmetry group for the friedmon is the dual su2. I agree with the suggestion to merge the wikipedia articles on einsteincartan theory ec and einsteincartansciamakibble theory ecsk. It modifies the geometrical structure of manifold and relaxes the notion of affine connection being symmetric. This modification was put forward in 1922 by elie cartan, before the discovery of spin. A geometric formulation of einstein maxwell theory in einstein cartan spacetime j. Cosmology with torsion nonsingular big bounce instead of big bang. The general theory of relativity the general theory of relativity is, as the name indicates, a generalization of the special theory of relativity. The universe and black holes in gravity with spin and torsion nikodem j. On the interpretation of the einstein cartan formalism 479 material charges and currents.
His theory was called einsteincartan theory of gravity ect. The faddeevpopov method of gauge xing is then discussed in ch. In hehls opinion einsteincartan theory is an even more beautiful theory than einstein s general relativity because of its relation to the poincare group. Cartan proposed einstein cartan theory ec to einstein in the 1920s because affine torsion is basic differential geometry. Einsteincartan theory is an extension of the standard formulation of. Of these, the einstein cartan model can be considered the prototype. Spin balances, energymomentum balances and weyssenho. The einsteincartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the. Einsteincartan theory and cosmology with torsion ikee. Since 1974, the search for quantum gravity has therefore provided the main motivation for the construction of gauge theories of gravity. Effective einstein cartan theory e einstein cartan lagrangian ec.
In the spacetime manifold of einstein cartan theory ect of gravitation, the expressions for the timelike kinematical parameters are derived and the propagation equation for expansion is obtained. The universe and black holes in gravity with spin and torsion. The coupling between the spin of elementary particles and torsion in the einsteincartan theory of gravity generates gravitational repulsion at extremely high densities in fermionic matter, approximated as a spin. Merge articles on einsteincartan theory and einsteincartansciamakibble theory.
Introduction much interest has been shown by many researchers in the theory of general relativity as a tool for studying the evolution and behaviour of various cosmological models. General relativity gr, also known as the general theory of relativity gtr, is the geometric theory of gravitation published by albert einstein in 1915 and the current description of gravitation in modern physics. Geometry and cosmology, the fundamental laws of classical mechanics, the newtonian worldsystem, the fundamental laws of optics, the fundamental laws of electrodynamics and einstein s special principle of relativity. Einsteincartan gravity in particle physics and cosmology. The theory was first proposed by elie cartan in 1922 and expounded in the following few years. What is the present status of the einsteincartan theory of. Derivation of the local lorentz gauge transformation of a. Einstein cartan theory, and its derivation from an action i think this is usually presented in the tetrad formalism, but obviously is a more specific thing and possibly harder to find. There are theories, however, in which curvature and torsion represent different gravitational degrees of freedom. About two decades ago, hehl11 gave, in einsteincartan theory, an.
Delphenich in the following pages, i propose to discuss, in a geometrically intuitive fashion, the unitary theory of gravitation and electricity that einstein, in collaboration with mayer, published in 1931 in the sitzungsberichte of the berlin academy 1. Emergent cosmos in einsteincartan theory springerlink. The einsteincartan theory ect of gravity is a modification of general relativity theory grt, allowing spacetime to have torsion, in addition to curvature, and relating torsion to the density of intrinsic angular momentum. Diether iii and joy christiany einstein centre for localrealistic physics, 15 thackley end, oxford ox2 6lb, united kingdom two of the major open questions in particle physics are.
He then constructed a new theory, called einstein cartan theory. Einstein hilbert field equation, restricted to gravitational theory in the early twenties, cartan suggested to einstein that the. The underlying spacetime of this theory is a riemann cartan. In this fascinating and thoughtful novel, we learn that this is more than possible. I standard cartan geometry is based on a model space, e. However, since we still have a theory made of the metric and its derivatives with no other variables thrown in as. I believe the term that has been adopted in the literature is einsteincartan theory. The einsteincartan theory can be derived using the following action. The genesis of the theory of relativity olivier darrigol cnrs. In einsteins theory of gravitation, mass directly influences the geometry but spin has no such dynamical effect. In theoretical physics, the einstein cartan theory, also known as the einstein cartan sciamakibble theory, is a classical theory of gravitation similar to general relativity but relaxing the assumption that the affine connection has vanishing antisymmetric part torsion tensor, so that the torsion can be coupled to the intrinsic angular momentum of matter, much in the same way in. Any modern physicist knows that this theory imposes a strict and general constraint on the laws of nature. Einsteincartan theory as an averaged theory of gravity. In contrast, einstein s equations tell you how the curvature responds to energymomentum and vice versa.
The structure equations give expressions for torsion and curvature in terms of the spin connection. In the spacetime manifold of einsteincartan theory ect of gravitation, the expressions for the timelike kinematical parameters are derived and the propagation equation for expansion is obtained. Finally, in the last section, our concluding remarks are represented. Einsteincartan theory is almost completely forgotten in the u. In theoretical physics, the einstein cartan theory, also known as the einstein cartan sciamakibble theory, is a classical theory of gravitation similar to general relativity.
In theoretical physics, the einsteincartan theory, also known as the einsteincartansciamakibble theory, is a classical theory of gravitation similar to general relativity. Spinning fluid cosmologies in einsteincartan theory. On the interpretation of the einsteincartan formalism. These papers can be found on the associated website, which is that of the alpha institute for advanced studies. In einstein cartan evans ece field theory 14 the fundamental field is the tetrad, which is a rank two mixed index tensor that transforms as such under the general coordinate transformation, and is thus generally covariant. In einstein s theory of gravitation, mass directly influences the geometry but spin. The ece theory has swept the world of physics, and has been read an accurately estimated thirty to fty million times in a decade.
We discuss the formalism of principal bundles, principal connections, curvature forms, gauge. The einsteincartan model of hories 2 is such a model. Cartan in 19231925, who suggested using an asymmetric linear connection. In standard model the particles with symmetry groups su3, u1 are stable, but for dual symmetry groups only particles with dual su2 group are stable. Request pdf einsteincartan theory the einsteincartan theory ect of. In the basic einstein cartan theory, in which the antisymmetric part of the connection is taken as independent additional degrees of freedom, the torsion is nondynamical. Just as the spacetime metric is sourced by the stressenergy tensor of the matter fields, torsion is sourced via the spin density tensor, whose physical effects become relevant at very high spin densities.
506 1601 241 525 338 564 873 349 381 737 366 1360 1380 66 954 1049 729 1357 109 150 548 347 947 331 286 519 915 1091 369 1040 239 1588 1560 602 129 1027 780 1141 713 764 904 1109