相关论文: Nonlinear distributional geometry and general rela…

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

Gravity with incorporation of additional dimensions and noncommutative geometry.

The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in…

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the…

Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that…

The non--linear dynamics of self--gravitating irrotational dust is analyzed in a general relativistic framework, using synchronous and comoving coordinates. Writing the equations in terms of the metric tensor of the spatial sections…

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…

Quasilinear perpendicular diffusion of charged particles in fluctuating electromagnetic fields is the focus of this paper. A general transport parameter for perpendicular diffusion is presented being valid for an arbitrary turbulence…

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…

We briefly discuss some possible cosmological implications of noncommutative geometry. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of other fields that are present in the…

For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…

In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…

A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of…

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation…

In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physicists and engineers who do research on J. F. Colombeau' theory of new generalized functions and its…

We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…

Vacuum gravitational fields invariant for a non Abelian Lie algebra generated by two Killing fields whose commutator is light-like are analyzed. It is shown that they represent nonlinear gravitational waves obeying to two nonlinear…

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors…