Peter Baekler

Topological gauge model of gravity with torsion

Abstract We generalize the topological massive gauge model of gravity to a three-dimensional Riemann-Cartan spacetime with torsion. Our Lagrangian consists of the familiar Einstein-Cartan term, the Chern-Simons three-form for the curvature and, in addition, of a new “translational” Chern-Simons term. An exact vacuum solution is derived with purely axial torsion and constant curvature.

Dynamical symmetries in topological 3D gravity with torsion

SummaryRecently two of us generalized the topological massive gauge model of gravity of Deser, Jackiw, and Templeton (DJT) by liberating its translational gauge degrees of freedom. Consequently, the newR3◯SO(1,2) gauge model «lives» in a 3-dimensional Riemann-Cartan space-time with torsion. The extended Lagrangian consists, of the familiar Einstein-Cartan term, the Chern-Simons 3-form for the curvature, and, in addition, of a new translational Chern-Simons term. In this article we uncover a «dynamical symmetry» of the new theory by inquiring how the two Noether identities, the two Bianchi identities, and the two field equations are interrelated to each other. This includes two important subcases in which the first Bianchi identity is mapped into the second one and the first (energy-momentum) Noether into the second (angular-momentum) Noether identity. As a furtherexact result, the topological gauge field equations imply a covariant Proca-type field equation, for the translational gauge potential,i.e. the coframe. Thus the theory encompasses massive gravitons, as in the DJT model.

A spherically symmetric vacuum solution of the quadratic Poincaré gauge field theory of gravitation with newtonian and confinement potentials

Abstract We derive a stationary spherically symmetric vacuum solution in the framework of the Poincare gauge field theory with a recently proposed quadratic lagrangian. We find a metric of the Schwarzschild-de Sitter type, both torsion and curvature are non vanishing, with torsion proportional to the mass and curvature proportional to the strong coupling constant κ . The metric exhibits two pieces, a newtonian potential describing the gravitational behavior of macroscopic matter, and a confining potential ∼ κr 2 presumably related to the strong-interaction properties of hadrons. To our knowledge this is a new feature of a classical solution of a Yang-Mills type gauge theory.

The exterior gravitational field of a charged spinning source in the poincaré gauge theory: A Kerr-newman metric with dynamic torsion☆

Abstract We present a new exact solution of the Poincare gauge theory, namely a charged Kerr-NUT metric with an effective cosmological constant which is consistently coupled to a dynamic torsion field. The solution is given in terms of an orthonormal basis in Boyer-Lindquist coordinates and depends on the constants m0 (mass), j0 (angular momentum), q0 (electric charge), and n0 (NUT parameter). Whereas m0,j0, and q0 can be specified arbitrarily, the NUT parameter and the effective cosmological constant are determined by the coupling constants of our model. The torsion of the solution is centered around the coordinate origin and vanishes asymptotically for large radial distance. For n0=0, we find the exterior gravitational field of a charged spinning source.

Kinky torsion in a poincaré gauge model of gravity coupled to a massless scalar field

Abstract For the quadratic Poincare gauge theory coupled to a massless scalar field (“Higgs field”) we study spherically symmetric solutions with duality properties of the Riemann-Cartan curvature. We find an exact solution with a localized scalar field and a torsion kink both residing in an open einsteinian microcosmos. Via a new dynamical mechanism, the asymptotically constant torsion compensates the bare “cosmological” constant.

A charged Taub-NUT metric with torsion: A new axially symmetric solution of the poincare gauge field theory

Abstract Within the framework of the Poincare gauge field theory, McCrea has recently discovered a Taub-NUT-like metric with torsion. The metric is axially symmetric, whereas the torsion turns out to be SO(3)-symmetric. We find the corresponding solution with an additional electric charge.

Effective Einsteinian gravity from Poincaré gauge field theory

Abstract The Poincare gauge theory of gravity should apply in the microphysical domain. Here we investigate its implications for macrophysics . Weakly self double dual Riemann-Cartan curvature is assumed throughout. It is shown that the metrical background is then determined by Einsteins field equations with the Belinfante-Rosenfeld symmetrized energy-momentum current amended by spin squared terms. Moreover, the effective cosmological constant can be reconciled with the empirical data by absorbing the corresponding constant curvature part into the dynamical torsion of recently found exact solutions. Macroscopically this extra torsion remains undetectable.

The Kummer tensor density in electrodynamics and in gravity

Abstract Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K i j k l . This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T i j k l , which is antisymmetric in its first two and its last two indices: T i j k l = − T j i k l = − T i j l k . Thus, K ∼ T 3 , see Eq. (46) . (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R i j k l of a Riemann–Cartan spacetime, then K ∼ R 3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group G L ( 4 , R ) and, subsequently, under the Lorentz group S O ( 1 , 3 ) .

The unique spherically symmetric solution of the U4-theory of gravity in the teleparallelism limit

Abstract Within the U 4 -theory of gravity in the teleparallelism limit we determine the metric and torsion tensor of a spherically symmetric fluid ball. We uniquely derive a Schwarzschild solution thereby establishing the validity of the Birkhoff theorem in this framework.

Rotating Black Holes in Metric-Affine Gravity

Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute space–time), we find, for a specific gravitational Lagrangian and by using prolongation techniques, a stationary axially symmetric exact solution of the vacuum field equations. This black hole solution embodies a Kerr–de Sitter metric and the post-Riemannian structures of torsion and nonmetricity. The solution is characterized by mass, angular momentum, and shear charge, the latter of which is a measure for violating Lorentz invariance.