arXiv research

Affine deformations of convex cones yield special spacetime structures.

New findings show Berwald Finsler spacetimes cannot be metrized.

A common approach to metric-affine, local Poincaré, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to altern…

A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves fo…

Researchers extend parametrization of Margulis spacetimes using strip deformations.

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

Solves Minkowski problem for affine invariant convex domains.

A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that every Margulis spacetime is orientable, even though S may be nonorientable. We classify Margulis spacetimes when S is homeomorphic…

A Margulis spacetime is a complete flat Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface S homotopy-equivalent to M. The purpose of this paper is to classify Margulis spacetimes when S is homeomorphic to a one-holed torus. We show that every such M decompo…

In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…

New spaces at infinity identified for Minkowski spacetime.

Jebsen-Birkhoff theorem extended to Berwald spacetimes.

Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional…

We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson-Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and div…

Odd connections on supermanifolds are defined and their properties studied.

In abstract Yang-Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instant…

Estimates how many times a star appears due to gravitational lensing.

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to expon…

A Margulis spacetime is a complete flat affine Lorentzian 3-manifold with free fundamental group. Associated to $M$ is a noncompact complete hyperbolic surface $Σ$. We study double extensions of $π_1 (M) \cong π_1 (Σ)$ when $Σ$ is homeomorphic to a projective plane minus two discs. We classify proper actions of this do…

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 resul…

New exact spherically symmetric vacuum solutions found in Finsler gravity.

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory, which allows us to prove that these models satisfy the principle of general local co…

Affine deformations of convex cones on projective surfaces.

The anholonomic frame method is generalized for non--Riemannian gravity models defined by string corrections to the general relativity and metric-affine gravity (MAG) theories. Such spacetime configurations are modeled as metric-affine spaces provided with generic off-diagonal metrics (which can not be diagonalized by …

Synthetic framework for null hypersurfaces in non-smooth spacetimes.

Study proves existence of multiple geodesics in a specific metric space.

A method to derive Lagrangians from field equations in metric-affine theories of gravity.

The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations…

The study identifies obstructions to global visibility of singularities in spacetimes.

Generalizes kinematical Lie algebras for isotropic spacetimes.

The thesis explores kinematical symmetries beyond Lorentzian spacetime.

In this article, we provide a necessary and sufficient criterion for proper actions on $\mathbb{H}^{n,n-1}$ in terms of certain special Anosov representations in $\mathsf{SO}(n,n)$. Moreover, we show that affine Anosov representations of any word hyperbolic group in $\mathsf{SO}(n,n-1)\ltimes\mathbb{R}^{2n-1}$ are infi…

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisym…

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…

The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.

The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

The study characterizes GRW spacetimes with gradient solitons and phantom era.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.

Study of quasilocal mass using isometric embedding in various spacetimes.

Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.

Characterizes a specific type of spacetime using vector fields.

We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric $H$--field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N--connection)…