Related papers: Recent results in mathematical relativity
This paper is a continuation of the papers [gr-qc/9409010, gr-qc/9505034]. A revision of the Einstein equation shows that its dynamic incompleteness, contrary to a popular opinion, cannot be circumvented by so-called coordinate conditions.…
In this contribution to the conference "Beyond Einstein: Historical Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century", we give a critical status report of attempts to explain the late accelerated expansion of the…
This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…
We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can…
We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an…
A short review of recent results on exact solutions in multidimensional cosmology and overview of reports at workshop in MG8 (held by the author) are presented.
We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
In hep-th/0506040 we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these…
There has been a recent resurgence of interest in the structure of the gravitational field at null infinity, sparked by new results on soft charges and infrared issues related to the S matrix theory in perturbative quantum gravity. We…
Since the past Iagrg meeting in December 2004, new developments in loop quantum cosmology have taken place, especially with regards to the resolution of the Big Bang singularity in the isotropic models. The singularity resolution issue has…
We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…