10 research outputs found
An axially symmetric solution of metric-affine gravity
We present an exact stationary {\it axially symmetric} vacuum solution of
metric-affine gravity (MAG) which generalises the recently reported spherically
symmetric solution. Besides the metric, it carries nonmetricity and torsion as
post-Riemannian geometrical structures. The parameters of the solution are
interpreted as mass and angular momentum and as dilation, shear and spin
charges.Comment: 5 pages, RevTe
Pleba\'nski-Demia\'nski-like solutions in metric-affine gravity
We consider a (non--Riemannian) metric--affine gravity theory, in particular
its nonmetricity--torsion sector ``isomorphic'' to the Einstein--Maxwell
theory. We map certain Einstein--Maxwell electrovacuum solutions to it, namely
the Pleba\'nski--Demia\'nski class of Petrov type D metrics.Comment: 12 pages of a LaTeX-fil
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 nonmetricity 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 nonmetricity. 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 (comprising torsion and
nonmetricity). All this is compared to the recent results of Vandyck.Comment: 9 pages, REVTeX, no figures; minor changes, version to be published
in Class. Quantum Gra
Non-Riemannian Gravity and the Einstein-Proca System
We argue that all Einstein-Maxwell or Einstein-Proca solutions to general
relativity may be used to construct a large class of solutions (involving
torsion and non-metricity) to theories of non-Riemannian gravitation that have
been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and
Quantum Gravit
Axial-Vector Torsion and the Teleparallel Kerr Spacetime
In the context of the teleparallel equivalent of general relativity, we
obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr
spacetime. It is shown that, in the slow rotation and weak field
approximations, the axial-vector torsion plays the role of the gravitomagnetic
component of the gravitational field, and is thus the responsible for the
Lense-Thirring effect.Comment: 9 pages, no figures, to appear in Class. Quant. Gra
Dark Matter Gravitational Interactions
We argue that the conjectured dark mater in the Universe may be endowed with
a new kind of gravitational charge that couples to a short range gravitational
interaction mediated by a massive vector field. A model is constructed that
assimilates this concept into ideas of current inflationary cosmology. The
model is also consistent with the observed behaviour of galactic rotation
curves according to Newtonian dynamics. The essential idea is that stars
composed of ordinary (as opposed to dark matter) experience Newtonian forces
due to the presence of an all pervading background of massive gravitationally
charged cold dark matter. The novel gravitational interactions are predicted to
have a significant influence on pre-inflationary cosmology. The precise details
depend on the nature of a gravitational Proca interaction and the description
of matter. A gravitational Proca field configuration that gives rise to
attractive forces between dark matter charges of like polarity exhibits
homogeneous isotropic eternal cosmologies that are free of cosmological
curvature singularities thus eliminating the horizon problem associated with
the standard big-bang scenario. Such solutions do however admit dense hot
pre-inflationary epochs each with a characteristic scale factor that may be
correlated with the dark matter density in the current era of expansion. The
model is based on a theory in which a modification of Einsteinian gravity at
very short distances can be expressed in terms of the gradient of the Einstein
metric and the torsion of a non-Riemannian connection on the bundle of linear
frames over spacetime. Indeed we demonstrate that the genesis of the model
resides in a remarkable simplification that occurs when one analyses the
variational equations associated with a broad class of non-Riemannian actions.Comment: 40 pages, 4 Postscript figure