Related papers: A new singularity theorem in relativistic cosmolog…
We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…
The Bakry-Emery generalized Ricci tensor arises in scalar-tensor gravitation theories in the conformal gauge known as the Jordan frame. Recent results from the mathematics literature show that standard singularity and splitting theorems…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space…
We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully…
A unified theory of all forces should be nonsingular. In such a unified theory, Einstein's general relativity will be a very low curvature effective theory. At larger curvatures, new terms will become important. The question then arises as…
In this talk we would like to review recent results on non-singular cosmological models. It has been recently shown that among stiff perfect fluid inhomogeneous spacetimes the absence of singularities is more common than it was expected in…
The spacetime singularities in classical general relativity are inevitable, which are also predicated by the celebrated singularity theorems. However, it is general belief that singularities do not exist in the nature and they are the…
We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum…
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…
It is proved that the Riemann tensor squared is divergent as $\tau \ra 0$ for a wide class of cosmological metrics with non-exceptional Kasner-like behaviour of scale factors as $\tau \ra 0$, where $\tau$ is synchronous time. Using this…
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…
Restrictions are obtained on the topology of a compact divergence-free null hypersurface in a four-dimensional Lorentzian manifold whose Ricci tensor is zero or satisfies some weaker conditions. This is done by showing that each null…
We investigate the cosmological applications of new gravitational scalar-tensor theories and we analyze them in the light of $H_0$ tension. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives in a…
In this paper we investigate the fate of the universe with an anisotropic background sourced by anisotropic matter. We see the behaviour of the Raychaudhuri Equation and investigate wheather a congrurence of time like geodesics focus to a…
In General Relativity without a cosmological constant a non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditions are assumed and regardless the considered solution…
A salient feature of Horava gravity is the anisotropic time variable. We propose an alternative construction of the spacetime manifold which naturally enables time anisotropy. We promote the role of curvature: the Ricci scalar R at a given…
We have extended our result on defocussing of world lines [1] by modifying gravity in the early epoch by a 5-d theory with scalar $\psi(r)$. The acceleration term in the Raychaudhuri equation has been shown to be positive for flat FRW…
Our focus is on a specific type-N space-time that exhibits closed time-like curves in general relativity theory within the framework of Ricci-inverse gravity model. The matter-energy content is solely composed of a pure radiation field, and…
We examine the solution of the constraints in spherically symmetric general relativity when spacetime has a flat spatial hypersurface. We demonstrate explicitly that given one flat slice, a foliation by flat slices can be consistently…
Normalizing the Einstein-Hilbert action by the volume functional makes the theory invariant under constant shifts in the Lagrangian. The associated field equations then resemble unimodular gravity whose otherwise arbitrary cosmological…