相关论文: Singularities and Conjugate Points in FLRW Spaceti…

We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states…

The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by…

The assumptions of the Hawking-Penrose singularity theorem are not covariant under field redefinitions. Thus we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with any other…

Theories with a non-minimal coupling between the space-time curvature and matter fields introduce an extra force due to the non-conservation of the matter energy momentum. In the present work the theoretical consistency of such couplings is…

The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat FRW geometry we derive the general nonsingular solution supported by a magnetic…

We investigate a non-minimally coupled scalar field theory within the framework of scalar-tensor gravity formulated in non-metricity geometry, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with…

We shall investigate the properties of a congruence of geodesics in the framework of Palatini f(R) theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that f(R) Palatini theories do…

Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the…

In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the…

In this work the possible geodesic completeness of an electromagnetic dipole wormhole is studied in detail. The space-time contains a curvature singularity and belongs to a class of solutions to the Einstein-Maxwell equations with a coupled…

We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of…

The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition.…

We study the conditions imposed on matter to produce a regular (non-singular) interior of a class of spherically symmetric black holes in the $f(T)$ extension of teleparallel gravity. The class of black holes studied is necessarily singular…

This paper presents an in-depth exploration of timelike free geodesics in spatially curved Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. A unified approach for these geodesics encompassing both radial and non-radial trajectories…

The works reported in this thesis primarily address the application of the Raychaudhuri equation in two intriguing problems in gravitational physics. These problems still lack universally accepted explanations. The first problem is related…

In this paper we provide a thorough classification of Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmological models in terms of the strong or weak character of their singularities according to the usual definitions. The classification…

We develop the theory of weighted Ricci curvature in a weighted Lorentz-Finsler framework and extend the classical singularity theorems of general relativity. In order to reach this result, we generalize the Jacobi, Riccati and Raychaudhuri…

Roger Penrose's 2020 Nobel Prize in Physics recognises that his identification of the concepts of "gravitational singularity" and an "incomplete, inextendible, null geodesic" is physically very important. The existence of an incomplete,…

This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The…

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition…