94 research outputs found
The Kummer tensor density in electrodynamics and in gravity
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, . This tensor density is, by
definition, a cubic algebraic functional of a tensor density of rank four
, which is antisymmetric in its first two and its last two
indices: . Thus,
, see Eq.(46). (i) If is identified with the
electromagnetic response tensor of local and linear media, the Kummer tensor
density encompasses the generalized {\it Fresnel wave surfaces} for propagating
light. In the reversible case, the wave surfaces turn out to be {\it Kummer
surfaces} as defined in algebraic geometry (Bateman 1910). (ii) If is
identified with the {\it curvature} tensor of a Riemann-Cartan
spacetime, then and, in the special case of general
relativity, reduces to the Kummer tensor of Zund (1969). This is related to the {\it principal null directions} of the curvature. We
discuss the properties of the general Kummer tensor density. In particular, we
decompose irreducibly under the 4-dimensional linear group
and, subsequently, under the Lorentz group .Comment: 54 pages, 6 figures, written in LaTex; improved version in accordance
with the referee repor
Multipole solutions in metric--affine gravity
Above Planck energies, the spacetime might become non--Riemannian, as it is
known fron string theory and inflation. Then geometries arise in which
nonmetricity and torsion appear as field strengths, side by side with
curvature. By gauging the affine group, a metric affine gauge theory emerges as
dynamical framework. Here, by using the harmonic map ansatz, a new class of
multipole like solutions in the metric affine gravity theory (MAG) is obtained.Comment: 13 pages, Revtex, to appear in Phys. Lett.
Extended Einstein-Cartan theory a la Diakonov: the field equations
Diakonov formulated a model of a primordial Dirac spinor field interacting
gravitationally within the geometric framework of the Poincar\'e gauge theory
(PGT). Thus, the gravitational field variables are the orthonormal coframe
(tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is
the Einstein-Cartan choice proportional to the curvature scalar plus a
cosmological term. In Diakonov's model the coframe is eliminated by expressing
it in terms of the primordial spinor. We derive the corresponding field
equations for the first time. We extend the Diakonov model by additionally
eliminating the Lorentz connection, but keeping local Lorentz covariance
intact. Then, if we drop the Einstein-Cartan term in the Lagrangian, a
nonlinear Heisenberg type spinor equation is recovered in the lowest
approximation.Comment: 13 pages, no figure
A square-torsion modification of Einstein-Cartan theory
In the present paper we consider a theory of gravity in which not only
curvature but also torsion is explicitly present in the Lagrangian, both with
their own coupling constant. In particular, we discuss the couplings to Dirac
fields and spin fluids: in the case of Dirac fields, we discuss how in our
approach, the Dirac self-interactions depend on the coupling constant as a
parameter that may even make these non-linearities manifest at subatomic
scales, showing different applications according to the value of the parameter
we have assigned; in the case of spin fluids, we discuss FLRW cosmological
models arising from the proposed theory.Comment: 21 page
Quadratic metric-affine gravity
We consider spacetime to be a connected real 4-manifold equipped with a
Lorentzian metric and an affine connection. The 10 independent components of
the (symmetric) metric tensor and the 64 connection coefficients are the
unknowns of our theory. We introduce an action which is quadratic in curvature
and study the resulting system of Euler-Lagrange equations. In the first part
of the paper we look for Riemannian solutions, i.e. solutions whose connection
is Levi-Civita. We find two classes of Riemannian solutions: 1) Einstein
spaces, and 2) spacetimes with metric of a pp-wave and parallel Ricci
curvature. We prove that for a generic quadratic action these are the only
Riemannian solutions. In the second part of the paper we look for
non-Riemannian solutions. We define the notion of a "Weyl pseudoinstanton"
(metric compatible spacetime whose curvature is purely Weyl) and prove that a
Weyl pseudoinstanton is a solution of our field equations. Using the
pseudoinstanton approach we construct explicitly a non-Riemannian solution
which is a wave of torsion in Minkowski space. We discuss the possibility of
using this non-Riemannian solution as a mathematical model for the graviton or
the neutrino.Comment: 25 pages, LaTeX2
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
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
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