Metric-affine Gauge Theory Of Gravity Research Articles

Dirac–Bergmann analysis and degrees of freedom of coincident f(Q)-gravity

We investigate the propagating degrees of freedom of f(Q)-gravity in a 4-dimensional space-time under the imposition of the coincident gauge by performing the Dirac–Bergmann analysis. In this work, we start with a top-down reconstruction of the metric-affine gauge theory of gravity based only on the concept of a vector bundle. Then, the so-called geometrical trinity of gravity is introduced and the role of the coincident GR is clarified. After that, we reveal relationships between the boundary terms in the variational principle and the symplectic structure of the theory in order to confirm the validity of the analysis for our studied theories. Then, as examples, we revisit the analysis of GR and its f(R∘)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathop {R}\\limits ^{\\circ }})$$\\end{document}-extensions. Finally, after reviewing the Dirac–Bergmann analysis of the coincident GR and that of f(T)-gravity, we perform the analysis of coincident f(Q)-gravity. Under the imposition of appropriate spatial boundary conditions, we find that, as a generic case, the theory has five primary, three secondary, and two tertiary constraint densities and all these constraint densities are classified into second-class constraint density; the number six is the propagating degrees of freedom of the theory and there are no longer any remaining gauge degrees of freedom. We also discuss the condition of providing seven pDoF as a generic case. The violation of diffeomorphism invariance of coincident f(Q)-gravity make it possible to emerge such several sectors.

Plebański-Demiański solutions with dynamical torsion and nonmetricity fields

We construct Plebański-Demiański stationary and axisymmetric solutions with two expanding and double principal null directions in the framework of Metric-Affine gauge theory of gravity. Starting from the new improved form of the metric with vanishing cosmological constant recently achieved by Podolský and Vrátný, we extend this form in the presence of a cosmological constant and derive the conditions under which the physical sources of the torsion and nonmetricity tensors provide dynamical contributions preserving it in Weyl-Cartan geometry. The resulting black hole configurations are characterised by the mass, orbital angular momentum, acceleration, NUT parameter, cosmological constant and electromagnetic charges of the Riemannian sector of the theory, as well as by the spin and dilation charges of the torsion and nonmetricity fields. The former is subject to a constraint representing a decoupling limit with the parameters responsible of axial symmetry, beyond which the geometry of the space-time is expected to be corrected.

Rotating Kerr-Newman space-times in metric-affine gravity

We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum. The corresponding Kerr-Newman-de Sitter solution is also compatible with a cosmological constant and additional electromagnetic fields.

Observational constraints in metric-affine gravity

We derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.

New models with independent dynamical torsion and nonmetricity fields

We propose a gravitational model which allows the independent dynamical behaviour of the torsion and nonmetricity fields to be displayed in the framework of Metric-Affine gauge theory of gravity. For this task, we derive a new exact black hole solution referred to this model which extends the role of torsion of the main well-known exact solutions based on Weyl-Cartan geometry and constitutes the first known isolated gravitational system characterized by a metric tensor with independent spin and dilation charges.

Solar constraints on new couplings between electromagnetism and gravity

The unification of quantum field theory and general relativity is a fundamental goal of modern physics. In many cases, theoretical efforts to achieve this goal introduce auxiliary gravitational fields, ones in addition to the familiar symmetric second-rank tensor potential of general relativity, and lead to nonmetric theories because of direct couplings between these auxiliary fields and matter. Here, we consider an example of a metric-affine gauge theory of gravity in which torsion couples nonminimally to the electromagnetic field. This coupling causes a phase difference to accumulate between different polarization states of light as they propagate through the metric-affine gravitational field. Solar spectropolarimetric observations are reported and used to set strong constraints on the relevant coupling constant k: k^2 < (2.5 km)^2.

Homogeneousisotropic models in the metric-affinegauge theory of gravity

Within the framework of the metric-affine gauge theory of gravitygravitational equations for homogeneous isotropic models are deduced andanalysed using the most general gravitational Lagrangian, including both ascalar curvature and terms quadratic in the curvature, torsion andnon-metricity tensors built without a Levi-Civita symbol. Restrictions onthe indefinite parameters of the gravitational Lagrangian, for whichdeduced equations lead to so-called generalized cosmological Friedmannequation for metrics and solutions in the Riemann-Cartan, Weyl,Weyl-Cartan spacetimes, are found. Some physical consequences arediscussed.

A Numeric Solution for Einstein's Gravitational Theory with Proca Matter and Metric-Affine Gravity

A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordstr"om type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity as its origin.

Nonlinear realizations of the diffeomorphism group in metric-affine gauge theory of gravity

The action of diffeomorphisms on coupled metric and spinor fields on a world manifold X is interpreted in terms of nonlinear realizations of the group GL∼+(4,R), the universal twofold covering group of the general linear group GL+(4,R), on the quotient manifold (GL∼+(4,R)×V)/SL(2,C), where SL(2,C) is the spin group and V is the spinor space. By using nonlinear realizations the connection of a metric-affine world manifold couples naturally to standard spinor fields. This enables us not to exceed the scope of usual spinor models as in the case in which infinite-dimensional representations of GL∼+(4,R) are considered. As an application, by starting from the familiar Lagrangian for spin-1/2 models and using the nonlinear realization method, a Lagrangian density for spinor fields which has GL∼+(4,R) as invariance group is constructed. The total Lagrangian density is obtained by adding the Lagrangian of the metric-affine gravity. The energy-momentum current associated with every vector field on the world manifold X is calculated explicitly. It turns out that spinor fields do not contribute to the corresponding superpotential, which takes a form similar to that obtained by Komar.

Computer algebra in gravity: Reduce-Excalc programs for (non-) Riemannian space-times. I

Computer algebra is applied to general relativity, to electrodynamics, and to gauge theories of gravity. As mathematical formalism we use the calculus of exterior differential forms and as computer algebra system Hearn's Reduce with Schrüfer's exterior form package Excalc. As a nontrivial example we discuss a metric of Plebański & Demiański (of Petrov type D) together with an electromagnetic potential and a triplet of post-Riemannian one-forms. This whole geometrical construct represents an exact solution of a metric-affine gauge theory of gravity. We describe a sample session and verify by computer that this exact solution fulfills the appropriate field equations. — Computer programs are described for the irreducible decomposition of (non-Riemannian) curvature, torsion, and nonmetricity.

Solitonic monopole solution in metric-affine gauge theory carrying Weyl charges

Examples in which spacetime might become non-Riemannian above Planck energies occur in string theory or in the very early universe in the inflationary model. The simplest such geometry is metric-affine geometry, in which nonmetricity appears as a field strength, side by side with curvature and torsion. In this paper we obtain a solitonic solution of the metric-affine gauge theory of gravity, which is endowed with shear and dilational Weyl charges.

BRST antifield treatment of metric-affine gravity

The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or non-metricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or non-metricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (which indicates torsion and non-metricity). All this is compared to the recent results of Vandyck.

Test matter in a spacetime with nonmetricity

Examples in which spacetime might become non-Riemannian appear above Planck energies in string theory or, in the very early Universe, in the inflationary model. The simplest such geometry is metric-affine geometry, in which nonmetricity appears as a field strength, side by side with curvature and torsion. In matter, the shear and dilation currents couple to nonmetricity, and they are its sources. After reviewing the equations of motion and the Noether identities, we study two recent vacuum solutions of the metric-affine gauge theory of gravity. We then use the values of the nonmetricity in these solutions to study the motion of the appropriate test matter. As a Regge-trajectory-like hadronic excitation band, the test matter is endowed with shear degrees of freedom and described by a world spinor.

An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges

The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses nonmetricity Q αβ and torsion T α as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation ⊕ shear ⊕ spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation ⊕ shear ⊕ spin charges.

Chern–Simons terms in metric-affine space-time: Bianchi identities as Euler–Lagrange equations

The metric-affine gauge theory of gravity encompasses a space-time with the following geometrical fields: coframe ϑα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four-forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)-scalars as well as exact forms derived from Chern–Simons type three-forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three-forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric-affine space-time.