Related papers: Mathematical General Relativity
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We consider time-dependent solutions of the Einstein-Maxwell equations using anti-de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief…
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 study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and…
A brief review is given of three recent results concerning classical solutions of gravitational theories: (1) With asymptotically anti de Sitter boundary conditions, there are matter theories satisfying the positive energy theorem which…
On the occasion of Sir Roger Penrose's 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent extension to Lorentzian metrics of low regularity. The latter is motivated by the quest to…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
There is no doubt that both the special and general theories of relativity capture the imagination. The anti-intuitive properties of the special theory of relativity and its deep philosophical implications, the bizzare and dazzling…
The de Sitter invariant special relativity is a natural extension of the usual Einstein special relativity. Within this framework a generalization of special relativity (SR) for the de Sitter space-time introduces a new length scale $R$,…
Recent advances, including gravitational wave detections and imaging of black hole shadows, have strongly validated general relativity. Nevertheless, ongoing cosmological observations suggest potential limitations of general relativity,…
We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR…
This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and…
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…
The Kerr-Newman metric is the unique vacuum solution of the General Relativistic field equations, in which any singularities or spacetime pathologies are hidden behind horizons. They are believed to describe the spacetimes of massive…
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…
It has been argued that generic classical perturbations to asymptotically de-Sitter Reissner-Nordtsr\"om (RN-dS) black holes may violate strong cosmic censorship conjecture. In this paper, we analyze whether quantum corrections can restore…
The strong proper time dilation and radial contraction in the gravitational field of compact sources leads to a frozen state of matter. It is shown that the falling particles and photons can not cross the gravitational radius due to the…
The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum…