Related papers: Regularity of curve integrable spacetimes

We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results…

In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…

We consider particle dynamics in singular gravitational field. In 2d spacetime the system splits into two independent gravitational systems without singularity. Dynamical integrals of each system define $sl(2,R)$ algebra, but the…

I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and…

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…

We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…

The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and…

General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…

Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and,…

The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold. We focus on the case of spherical systems, which are…

I describe several conceptual aspects of a particular paradigm which treats the field equations of gravity as emergent. These aspects are related to the features of classical gravitational theories which defy explanation within the…

We discuss here the issue of regularity of initial data for dynamical spherically symmetric massless scalar field models in a spacetime. Generalizing the known solutions of Einstein equations given in this case by Wyman and Roberts, we…

It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in arXiv:2008.09387. In this paper, we start to extend this…

After reviewing the definitions of classical and quantum singularities, it is shown by example that if zeroth-order curvature invariants are regular, a diverging higher-order curvature invariant does not necessarily imply the existence of a…

A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…

Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent…

I investigate spacetime singularities from the point of view of the wavefunction of the universe. In order to extend the classical notion of geodesic incompleteness one has to include the proper time of an observer as a degree of freedom in…

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…

By constructing a model of spacetime having a strong curvature singularity in which causal geodesics are complete, but more generic causal curves are not, we explicitly show that some electrostatic field configurations on that background…

The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a…