Dynamical Torsion Research Articles

Wavelike exact solutions of R+R2+Q2 gravity

The spinorial methods are applied to the analysis of the wavelike exact solutions of the gauge theory of gravitation with dynamical torsion. The N-type plane-fronted metric-torsion-electromagnetic wave for the most general quadratic in the torsion and curvature Lagrangian with nonvanishing cosmological constant are presented. A series of non-plane-fronted exact solutions with nontrivial torsion are found also. The question about equivalence of equations of the gauge theory of gravitation and the general relativity in the vacuum torsionless case are clarified. The example of non-Einsteinian vacuum solution for exceptional choice of cosmological constant are presented.

Two-Dimensional Gravity and Nonlinear Gauge Theory

We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincaré algebra, which is the new Yang-Mills-like formulation of the gravitational theory. As typical examples, we investigate R 2 gravity with dynamical torsion and generic form of "dilaton" gravity. The supersymmetric extension of this theory is also discussed.

NON-EINSTEINIAN GRAVITY IN d=2: SYMMETRY AND CURRENT ALGEBRA

For a geometric theory with dynamical torsion an absolutely conserved quantity can be related to a Noether current for a peculiar field dependent off-shell (global) symmetry. Moreover the nonlinear deformed iso(2,1) symmetry in phase space discovered previously, for which that conserved quantity is one element of the center, can be reinterpreted as a current algebra.

QUANTUM FUNCTIONAL INTEGRATION OF NON-EINSTEINIAN GRAVITY IN d=2

Complete integrability of R2 gravity with dynamical torsion in d=2 is also found in the quantum case, provided the light cone gauge is chosen. In our present work the path integral is derived from a covariant canonical and a canonical BRS approach. In the latter case and in that particular gauge all quantum effects — including Faddeev-Popov ghosts — vanish within the most simple topological setting which emphasizes local properties only. In the covariant canonical approach and with respect to a previous all-order perturbative analysis, the results are found to differ only by a counterterm.

Gauge Theory Based on Quadratic Lie Algebras and 2D Gravity with Dynamical Torsion

We construct a two·dimensional field theory with gauge symmetry based on quadratically nonlinear extension of Lie algebras. The case of Lorentz·covariant quadratic extension of the Poincare algebra turns out to give the Yang·MilIs·like formulation of R2 gravity with dynamical torsion. This paper provides a more detailed characterization of the deformation stated above. For that purpose, we first construct a two-dimensional gauge theory based on quadratically nonlinear extension of Lie algebras.*) We make use of 'nonlinear' gauge fields considered in Ref. 5), and propose an action invariant under their 'non­ linear' gauge transformations. We then consider Lorentz-covariant quadratic extension of the Poincare algebra and our 'nonlinear' gauge theory based on it. The theory turns out to be none other than the Yang-Mills-like formulation of R2 gravity with dynamical torsion we have investigated.

Gauge Theory Based on Quadratic Lie Algebras and 2D Gravity with Dynamical Torsion

We construct a two-dimensional field theory with gauge symmetry based on quadratically nonlinear extension of Lie algebras. The case of Lorentz-covariant quadratic extension of the Poincaré algebra turns out to give the Yang-Mills-like formulation of R2 gravity with dynamical torsion.

New constraints in dynamical torsion theory

The most general Lagrangian for dynamical torsion theory quadratic in curvature and torsion is considered. We impose two simple and physically reasonable constraints on the solutions of the equations of motion: (i) there must be solutions with zero curvature and nontrivial torsion and (ii) there must be solutions with zero torsion and non covariantly constant curvature. The constraints reduce the number of independent coupling constants from ten to five. The resulting theory contains Einstein's general relativity and Weitzenbock's absolute parallelism theory as the two sectors.

Quantum Gravity with Dynamical Torsion in Two Dimensions

One of the main reasons for considering two-dimensional gravity is an expectation that it may provide a conceptual laboratory for investigation of quantum gravity in higher dimensions. In particular, dynamical coupling of quantum matter fields seems manageable only in two spacetime dimensions. However, as long as pure gravity is concerned, it is so special in two dimensions that it bears little resemblance to pure gravity in three or more dimensions. Naive counting gives a negative degree of freedom for the metric field gPJJ with general covariance. Indeed, in two dimensions, the Einstein tensor GpJJ=RpJJ-(1/2)gpJJR vanishes identically, and hence there is no sensible Einstein equation at all. The introduction of an additional scalar field (J makes it possible to define a nontrivial theoryl)

Quantum Gravity with Dynamical Torsion in Two Dimensions

Quantum Gravity with Dynamical Torsion in Two Dimensions

Axion hair and dynamical torsion from anomalies

Recent studies have shown that black holes can indeed have hair in gravitational theories beyond minimal Einstein gravity. The hair is associated with the axion and dilaton of string theory, whose gauge and gravitational structure is richer than the conventional, minimally coupled theory. The axion in this case also has a dual rôle as a dynamical degree of freedom of the torsion. In this paper we suggest that there is a large class of models for which a torsion may be transmuted to an axion, and black holes develop hair. Indeed we show that even a model as simple as QED on a torsionful background space-time gives rise to axionic hair. We discuss this phenomenon and its implications.

Renormalization of R2 gravity with dynamical torsion in d = 2

Expressed in terms of zweibein and spin-connection, non-einsteinian gravity in d = 2 resembles a gauge theory with noncompact group and with nonpolynomial self-interactions. We show that this theory, nevertheless, is renormalizable because an infinite set of counterterms in the effective action may be expressed by one renormalizable quantity. Our analysis is based upon the use of a light-cone gauge where the UV behaviour, but especially also severe IR problems are more amenable to analysis than in a covariant gauge.

General analytic solution of R2 gravity with dynamical torsion in two dimensions.

Using light-cone variables, we show that ${R}^{2}$ gravity with dynamical torsion in two dimensions is one of the rare field theories whose complete classical solution in closed form can be obtained. It fulfils an invariant relation between the cosmological constant, the curvature scalar, and the scalar formed by the torsion tensor. We conjecture that this relation, interpreted as a local conservation law, is closely connected to the integrability of the theory. The solutions may possess a rich spectrum of singularities in curvature and torsion. Special cases, including one with nonvanishing torsion, can be used to elucidate some physical properties of the solution where by "physical" we imply the validity of concepts from general relativity such as measurements of distances and times and of extremal trajectories of a scalar test particle.

Complete integrability of two-dimensional gravity with dynamical torsion

The most general Lagrangian for two-dimensional gravity with dynamical torsion is considered. A general solution of the system of nonlinear equations of motion is found. Also found is a global solution of the Cauchy problem.

Two-dimensional gravity with dynamical torsion and strings

A two-dimensional theory of gravity with dynamical metric and torsion that was proposed in the context of string theory is considered. We analyse the equations of motion following from a Lagrangian quadratic in curvature and torsion, L = R 2 + T 2 + λ. The equations of motion are reduced to a system of equations for two scalar fields which in a particular case yields the Liouville equation. We have found and analysed stationary solutions with nontrivial torsion. It is proved that equations for extremals defining trajectories of pointlike spinless particles are completely integrable. A singularity of stationary space-time with nontrivial torsion has a repulsive character contrary to that of a black hole, and no particle can penetrate through it. Modification of the string theory due to the addition of the gravity Lagrangian is discussed.

Two-dimensional gravity with dynamical torsion and strings: M. O. Katanaev and I. V. Volovich. Steklov Mathematical Institute, Vavilova Street 42, GSP-1, 117966 Moscow, USSR

Two-dimensional gravity with dynamical torsion and strings: M. O. Katanaev and I. V. Volovich. Steklov Mathematical Institute, Vavilova Street 42, GSP-1, 117966 Moscow, USSR

Fermions in a two-dimensional theory of gravity with dynamical metric and torsion

We propose a new model which reduces a two-dimensional gravitational model with dynamical metric and torsion in a conformal gauge. We also find the instanton-like solutions and discuss their symmetry properties and eigenmodes.

New ghost-free extensions of general relativity

The method of algebraic extension is shown to yield a large class of gravitational theories which are extensions of general relativity. Requiring positivity of energy in the flat-space limit of such theories provides some constraints, but a large set of theories of potential phenomenological interest survives this condition. Explicit examples of such theories include the non-symmetric gravitational theory of Moffat, algebraically extended Hilbert gravity and a one-parameter family of theories with dynamical torsion. In general such theories do not alter general relativistic post-Newtonian predictions for time delay experiments; rather they alter the non-linearities of the post-Newtonian gravitational potential. Such effects may be probed by measuring periastron shifts, as in the eclipsing binary systems Di Her and AS Cam, as well as in the binary pulsar PSR 1913+16.

Instanton and eigenmodes in a two-dimensional theory of gravity with torsion

Instanton-like solutions characterizing the geometric structure of the manifold are found to be in a two-dimensional theory of gravity with dynamical metric and torsion in the context of string theory. The eigenmodes for fluctuations of the solutions of the equations are also investigated and it has been shown that these solutions are stable.

Kinetic part of dynamical torsion theory

A canonical Hamiltonian for a theory of dynamical torsion is constructed in the time gauge for the tetrad field. Restrictions in the form of inequalities on the coupling constants of the nine-parameter Lagrangian under which the quadratic form in the momenta is positive definite for all components of the tetrad field and Lorentz connection are found.

Hidden symmetries of Kaluza-Klein theories

It is shown that the introduction of dynamical torsion in Kaluza-Klein theories makes it possible to increase the number of gauge fields extracted from the Lagrangian without increasing the number of additional dimensions. An example of spontaneous compactification of a studied model is considered.