Related papers: Spacetime Defects: Torsion Loops
This study examines the formulation of a singularity theorem for timelike curves including torsion, and establishes the foundational framework necessary for its derivation. We begin by deriving the relative acceleration for an arbitrary…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…
In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…
We investigate Lorentzian spacetimes where all zeroth and first order curvature invariants vanish and discuss how this class differs from the one where all curvature invariants vanish (VSI). We show that for VSI spacetimes all components of…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature $ \delta $-singularities are found while Cartan torsion is given by Heaviside…
A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
General relativity is incomplete because it cannot describe quantum effects of space-time. The complete theory of quantum gravity is not yet known and to date no observational evidence exists that space-time is quantized. However, in most…
Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat…
Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to…
The appealing connection between non-Euclidean geometries and defects in solids is brought forth in this article. Drawing a correspondence between the nature of a defect and a specific geometric property of the material space not only…
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we…
Cosmology with non-perturbative quantum corrections resulting from torsion is considered. It is shown that the evolution of closed, open and flat Universes is changed because of the presence of a non-zero dispersion of quantum torsion. The…
This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is…
Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the…
We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum…
There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…
We consider space-times which are asymptotically flat at spacelike infinity, i^0. It is well known that, in general, one cannot have a smooth differentiable structure at i^0, but have to use direction dependent structures. Instead of the…
We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some…