A numeric solution for metric-affine gravity and Einstein's gravitational theory with Proca matter

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.Comment: LaTeX2e, 20 pages, 22 figure

PP-waves with torsion and metric-affine gravity

A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves for constructing new explicit vacuum solutions of quadratic metric-affine gravity.Comment: 17 pages, LaTeX2

Chiral Asymmetry and the Spectral Action

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter

Asymptotic charges in 3d gravity with torsion

We discuss some new developments in three-dimensional gravity with torsion, based on Riemann-Cartan geometry. Using the canonical approach, we study the structure of asymptotic symmetry, clarify its fundamental role in defining the gravitational conserved charges, and explore the influence of the asymptotic structure on the black hole entropy.Comment: 6 pages, LATEX file (+jpconf.cls,jpconf11.clo), Talk presented at Constrained Dynamics and Quantum Gravity 05, Cala Gonone (Sardinia, Italy), September 12-16, 200

Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence

The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction term. The characterization of tetrad fields as reference frames is addressed in the context of the Kerr space-time. It is also pointed out that Einstein's version of the principle of equivalence does not preclude the existence of a definition for the gravitational energy-momentum density.Comment: 17 pages, Latex file, no figure; minor correction in eq. (14), three references added, to appear in the GRG Journa

Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part

We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$ and the curvature pseudo-scalar $X$ linearly and quadratically (including an $RX$ term) and (ii) pieces quadratic in the torsion {\it vector} $\cal V$ and the torsion {\it axial} vector $\cal A$ (including a ${\cal V}{\cal A}$ term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms (`world') and of parity violating terms (`shadow world'). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic `torsion cosmologies' of Shie-Nester-Yo (2008) and Chen et al.\ (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces $R(t)$ and $X(t)$. Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.Comment: Latex computerscript, 25 pages; mistakes corrected, references added, notation and title slightly changed; accepted by Phys. Rev.

Mass and Spin of Poincare Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra

Isomorphism between Non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories

We extend the recently proved relation between certain models of Non-Riemannian gravitation and Einstein- Proca-Weyl theories to a class of Scalar gravity theories. This is used to present a Black-Hole Dilaton solution with non-Riemannian connection.Comment: 13 pages, tex file, accepted in Class. Quant. Gra

Hamiltonian Poincar\'e Gauge Theory of Gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as the local spacetime group of the gravitational gauge theory, with $SO(3)$ as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary $SO(3)$ vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.Comment: 38 pages, plainTe

Torsion nonminimally coupled to the electromagnetic field and birefringence

In conventional Maxwell--Lorentz electrodynamics, the propagation of light is influenced by the metric, not, however, by the possible presence of a torsion T. Still the light can feel torsion if the latter is coupled nonminimally to the electromagnetic field F by means of a supplementary Lagrangian of the type l^2 T^2 F^2 (l = coupling constant). Recently Preuss suggested a specific nonminimal term of this nature. We evaluate the spacetime relation of Preuss in the background of a general O(3)-symmetric torsion field and prove by specifying the optical metric of spacetime that this can yield birefringence in vacuum. Moreover, we show that the nonminimally coupled homogeneous and isotropic torsion field in a Friedmann cosmos affects the speed of light.Comment: Revtex, 12 pages, no figure