Related papers: Nonassociative geometry: Friedmann-Robertson-Walke…
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of…
We review a gravitational model based on noncommutative geometry and the spectral action principle. The space-time geometry is described by the tensor product of a four-dimensional Riemanian manifold by a discrete noncommutative space…
Principles of a new approach (binary geometrophysics) are presented to construct the unified theory of spacetime and the familiar kinds of physical interactions. Physically, the approach is a modified S-matrix theory involving ideas of the…
This paper provides an analytical treatment of accelerated and geodesic motion within the framework of the Friedmann -Lemaitre-Robertson-Walker (FLRW) spacetime. By employing conformal time transformations we manage to convert second order…
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…
A model for an expanding noncommutative acoustic fluid analogous to a Friedmann-Robertson-Walker geometry is derived. For this purpose, a noncommutative Abelian Higgs model is considered in a (3+1)-dimensional spacetime. In this scenario,…
In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time,, denoted by $L^4_1(f,c)$, having positive relative nullity. First, we give the necessary and sufficient conditions for such space-like and…
Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time…
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…
We make an attempt to develop "noncommutative algebraic geometry" in which noncommutative affine schemes are in one-to-one correspondence with associative algebras. In the first part we discuss various aspects of smoothness in affine…
Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lema\^{i}tre-Robertson-Walker geometry. In…
In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In…
We combine notions of a maximal curvature scale in nature with that of a minimal curvature scale to construct a non-singular Schwarzschild-de Sitter black hole. We present an exact solution within the context of two-dimensional dilaton…
We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$ and its unitary irreducible representations. We solve the Klein-Gordon equation in…
We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed…
We show that a non-commutative structure arises naturally from perturbative quantum gravity in a de Sitter background metric. Our work builds on recent advances in the construction of observables in highly symmetric background spacetimes…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…
In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short…
In order to get a better understanding of holographic properties of gravitational theories with a vanishing cosmological constant, we analyze in detail the relation between asymptotically anti-de Sitter and asymptotically flat spacetimes in…