Related papers: Static- and Stationary-complete Spacetimes: Algebr…
Stationary subspace analysis (SSA) searches for linear combinations of the components of nonstationary vector time series that are stationary. These linear combinations and their number defne an associated stationary subspace and its…
The model of a stationary universe and the notion of local times presented in [10] are reviewed with some alternative formulation of the consistent unification of the Riemannian and Euclidean geometries of general relativity and quantum…
The notion of singular generalized Finsler spacetime and singular generalized Berwald spacetime are introduced and their relevance for the description of classical gravity discussed. A method to construct examples of such generalized…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
We provide a general method for studying a manifestly covariant formulation of $p$-form gauge theories on the de Sitter space. This is done by stereographically projecting the corresponding theories, defined on flat Minkowski space, onto…
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a…
We construct globally hyperbolic spacetimes such that each slice $\{t=t_0\}$ of the universal time $t$ is a model space of constant curvature $k(t_0)$ which may not only vary with $t_0\in\mathbb{R}$ but also change its sign. The metric is…
We analyse properties of general stationary and axisymmetric spacetimes, with a particular focus on circularity -- an accidental symmetry enjoyed by the Kerr metric, and therefore widely assumed when searching for rotating black hole…
A theory governing the metric and matter fields in spacetime is {\it locally causal} if the probability distribution for the fields in any region is determined solely by physical data in the region's past, i.e. it is independent of events…
This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing…
The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
The construction of the cylinder at spatial infinity for stationary spacetimes is considered. Using a specific conformal gauge and frame, it is shown that the tensorial fields associated to the conformal Einstein field equations admit…
The periodic standing wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for ``helical scalars,'' fields that…
I discuss empty space, as it appears in the physical foundations of relativistic field theories and in the semiclassical study of isolated systems. Of particular interest is the relationship between empirical measurements of the…
We explore the question of how to probe the vacuum structure of space time by a massive scalar field through interaction with background gravitons. Using the $\Gamma$-regularization for the in-/out-state formalism, we find the effective…
We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Let $(M,g)$ be a spacetime which admits a complete timelike conformal Killing vector field $K$. We prove that $(M,g)$ splits globally as a standard conformastationary spacetime with respect to $K$ if and only if $(M,g)$ is distinguishing…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…