相关论文: Future Singularities and Completeness in Cosmology

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature…

The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding…

We show that a globally hyperbolic spacetime containing a trapped surface and satisfying the strong energy condition and a condition on certain radial tidal forces must be timelike geodesically incomplete. This constitutes a "timelike"…

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…

The discovery of universe's late-time acceleration and dark energy has overseen a great deal of research into cosmological singularities and in this brief review, we discuss all the prominent developments in this field for the best part of…

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum…

Singularities in General Relativity are regions where the description of spacetime in terms of a pseudo-Riemannian geometry breaks down. The theory seems unable to predict the evolution of the physical degrees of freedom around and beyond…

We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if…

A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive…

Following the observational evidence for cosmic acceleration which may exclude a possibility for the universe to recollapse to a second singularity, we review alternative scenarios of its future evolution. Although the de Sitter asymptotic…

We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…

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…

We investigate a particular regularization of big bang singularity, which remains within the domain of 4-dimensional general relativity but allowing for degenerate metrics. We study the geodesics and geodesic congruences in the modified…

Singularities in any physical theory are either remarkable indicators of the unknown underlying fundamental theory, or indicate a change in the description of the physical reality. In General Relativity there are three fundamental kinds of…

We use a method of linearization to study the emergence of the future cosmological singularity characterized by finite value of the cosmological radius. We uncover such singularities that keep Hubble parameter finite while making all higher…

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the…

Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…

Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…

This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…

We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature $K$ are…