相关论文: Geometric description of lightlike foliations by a…
The homogeneous and isotropic radiation dominated universe, following the inflationary stage, is expressed as a spherically symmetric and inhomogeneous spacetime upon a power law type conformal transformation of the null (cosmological)…
We study the dynamics of gauge theory and general relativity using fields of local observers, thus maintaining local Lorentz symmetry despite a space/time splitting of fields. We start with Yang--Mills theory, where observer fields are…
This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange…
We study codimension-two spacelike submanifolds in Lorentzian spacetimes that admit umbilical lightlike normal directions. We show that such submanifolds are subject to strong geometric and topological constraints, establishing explicit…
4-dimensional optics is here introduced axiomatically as the space that supports a Universal wave equation which is applied to the postulated Higgs field. Self-guiding of this field is shown to produce all the modes necessary to provide…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These…
A procedure avoiding any integration of the null geodesic equations is used to derive the direction of light propagation in a three-parameter family of static, spherically symmetric spacetimes within the post-post-Minkowskian approximation.…
We discuss a new formalism for light propagation which can be used within the regime of validity of geometric optics, but with no limitation on the scales of interest: from inside the Galaxy to the ultra-large scales of cosmology. One of…
Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized…
Hamiltonian gravity, relying on arbitrary choices of "space," can obscure spacetime symmetries. We present an alternative, manifestly spacetime covariant formulation that nonetheless distinguishes between "spatial" and "temporal" variables.…
Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though…
The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background…
The laws of geometric optics and their corrections are derived for scalar, electromagnetic, and gravitational waves propagating in generic curved spacetimes. Local peeling-type results are obtained, where different components of…
The space-time foliation Sigma compatible with the gravitational field g on a 4-manifold M determines a fibration pi of M, pi : M -> N is a surjective submersion over the 1-dimensional leaves space N. M is then written as a disjoint union…
We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
Fermi co-ordinates are proper co-ordinates of a local observer determined by his trajectory in space-time. Two observers at different positions belong to different Fermi frames even if there is no relative motion between them. Use of Fermi…
The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold $(M, c)$ endowed with a pseudoconformal structure $c = CO (2, 2)$. They prove that a lightlike hypersurface $V \subset (M, c)$ bears a foliation formed…