Chirality in Affine Spaces and in Spacetime

Chirality in Gravitational and Electromagnetic Interactions with Matter

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigenmodes of a chirality operator. Complex gravitational pulse solutions t…

Affine Symmetry, Geodesics, and Homogeneous Spacetimes

We show that the conservation laws for the geodesic equation which are associated to affine symmetries can be obtained from symmetries of the Lagrangian for affinely parametrized geodesics according to Noether's theorem, in contrast to claims found in the literature. In particular, using Aminova's classification of affine motions of Lorentzian manifolds, we show in detail how affine motions define generalized symmetries of the geodesic Lagrangian. We compute all infinitesimal proper affine symmetries and the corresponding geodesic conservation laws for all homogeneous solutions to the Einstein…

On the non metrizability of Berwald Finsler spacetimes

We investigate whether Szabo's metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern-Rund connection defines an affine connection on the underlying manifold), then it is affinely equivalent to a Riemann space, meaning that its affine connection is the Levi-Civita connection of some Riemannian metric. We show for the first time that this result does not extend to Finsler spacetimes. More precisely, we find a large class of Berwald spacet…

仿射向量场的反对称张量推广

Antisymmetric tensor generalizations of affine vector fields

仿射向量场的张量推广称为对称和反对称仿射张量场作为时空的对称性进行了讨论。我们回顾了对称的性质，这已经在早期的工作中研究，并调查反对称的性质，这是本文的主题。证明了反对称仿射张量场与沿测地线输运的低秩反对称张量场密切相关。证明了在$n$维上线性无关秩$p$反对称仿射张量场的个数是由$(n+1)!/p!(n-p)!$有界的.我们还导出了反对称仿射张量场的可积性条件。利用可积性条件讨论了各种时空上反对称仿射张量场的存在性。

Reformulation of Special Relativity and Electromagnetism in terms of Reference Frames defined as maps from spacetime onto affine spaces

A reference frame on a set $M$ is given by a 3-dimensional euclidean space $E$, a function from $M$ to $E$, a 1-dimensional affine space $A$ and a function from $M$ to $A$. The definition allows an intuitive and coordinate-free formulation of Newtonian mechanics, special relativity and electromagnetism in terms of frames instead of coordinates. In particular, the postulate of a set of charts on $M$ (an atlas) is replaced by the postulate of a set of frames. Then the charts can be re-obtained through the choice of affine coordinates. In addition, units enter the theory as elements of positive s…

Ascribing quantum system to Schwarzschild spacetime with naked singularity

We quantize the Schwarzschild spacetime with naked singularity using the affine coherent states quantization method. The novelty of our approach is quantization of both temporal and spatial coordinates. Quantization smears the gravitational singularity indicated by the Kretschmann invariant avoiding its localization in the configuration space. This way we resolve the singularity problem of considered spacetime at quantum level.