Related papers: Rigidity Results in General Relativity: a Review
The singularity of the solutions obtained before in the teleparallel theory of gravitation is studied. Also the stability of these solutions is studied using the equations of geodesic deviation. The condition of stability is obtained. From…
While in general relativity black holes can be freely embedded into a cosmological background, the same problem in brane-worlds is much more cumbersome. We present here the results obtained so far in the explicit constructions of such…
In this article, we study regular scale-dependent black holes as gravitational lenses. We obtain the deflection angle in the strong deflection limit, from which we calculate the positions and the magnifications of the relativistic images.…
It is thought that the final product of the gravitational collapse is a Kerr black hole and astronomers have discovered several good astrophysical candidates. While there is some indirect evidence suggesting that the latter have an event…
We review the foundations of Einstein's general theory of relativity, discuss recent progress in the tests of relativistic gravity, and present motivations for new generation of high-accuracy gravitational experiments. We discuss the…
General relativity (GR) passed many astronomical tests but in majority of them GR predictions have been tested in a weak gravitational field approximation. Around 50 years ago a shadow has been introduced by J. Bardeen as a purely…
Do black holes rotate, and if yes, how fast? This question is fundamental and has broad implications, but still remains open. There are significant observational challenges in current spin determinations, and future facilities offer…
We study the time dependence of the generalized complexity of Lovelock black holes using the ``complexity = anything" conjecture, which expands upon the notion of ``complexity = volume" and generates a large class of observables. By…
After recalling the conceptual foundations and the basic structure of general relativity, we review some of its main modern developments (apart from cosmology) : (i) the post-Newtonian limit and weak-field tests in the solar system, (ii)…
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics.…
The uniqueness and rigidity theorems assert that the asymptotically flat, vacuum, stationary rotating black hole solution in general relativity must be the Kerr solution, exhibiting novel symmetries such as axisymmetry and circularity. In…
Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical…
The article summarizes the observational evidence for the existence of massive black holes, as well as the current knowledge about their abundance, their mass and spin distributions, and their cosmic evolution within and together with their…
The existence of black holes in the Universe is nowadays established on the grounds of a blench of astrophysical observations, most notably those of gravitational waves from binary mergers and the imaging of supermassive objects at the…
Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
After a brief introduction to the black hole stability problem, we outline our recent proof of the linear stability of the non-extreme Kerr geometry.
We use exact results in a new approach to quantum gravity to study the effect of quantum loop corrections on the behavior of the metric of space-time near the Schwarzschild radius of a massive point particle in the Standard Model. We show…
An open problem in general relativity has been to construct an asymptotically flat solution to a reasonable Einstein-matter system containing a black hole in the future and yet past-causally geodesically complete, in particular, containing…
Unless the reality of spacetime singularities is assumed, astrophysical black holes cannot be identical to their mathematical counterparts obtained as solutions of the Einstein field equations. Mechanisms for singularity regularization…