Related papers: On Breakdown Criteria for Nonvacuum Einstein Equat…
The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce…
Misner spacetime is among the simplest solutions of Einstein's equation that exhibits a Cauchy horizon with a smooth extension beyond it. Besides violating strong cosmic censorship, this extension contains closed timelike curves. We analyze…
We consider weakly regular Gowdy-symmetric spacetimes on T3 satisfying the Einstein-Euler equations of general relativity, and we solve the initial value problem when the initial data set has bounded variation, only, so that the…
We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such…
We study closed $n$-dimensional manifolds of which the metrics are critical for quadratic curvature functionals involving the Ricci curvature, the scalar curvature and the Riemannian curvature tensor on the space of Riemannian metrics with…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
Post-Newtonian theory was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone…
It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the…
The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper…
New symmetries have been found in Einstein-Maxwell spacetimes. New symmetries have also been found in imperfect fluid curved spacetimes. We will prove in this paper that we can extend these symmetries to spacetimes with higher curvature…
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to…
We discuss the structure of microcanonical ensembles in inertial and non-inertial frames attached to a confined system of positive energy particles in curved spacetime. Under certain physically reasonable assumptions that ensure the…
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved…
In this paper we discuss and prove $\epsilon$-regularity theorems for Einstein manifolds $(M^n,g)$, and more generally manifolds with just bounded Ricci curvature, in the collapsed setting. A key tool in the regularity theory of…
The Einstein field equation as an equation of state of a thermodynamical system of spacetime is reconsidered in the present Letter. We argue that a consistent interpretation leads us to identify scalar curvature and cosmological constant…
In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical…
A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless…
The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary…