Related papers: From Geometry to Numerics: interdisciplinary aspec…
The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…
While singularities are inevitable in the classical theory of general relativity, it is commonly believed that they will not be present when quantum gravity effects are taken into account in a consistent framework. In particular, the…
In this thesis three separate problems relevant to general relativity are considered. Methods for algorithmically producing all the solutions of isotropic fluid spheres have been developed over the last five years. A different and somewhat…
These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…
We propose a new parametric framework to describe in generic metric theories of gravity the spacetime of spherically symmetric and slowly rotating black holes. In contrast to similar approaches proposed so far, we do not use a Taylor…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike…
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
The possible existence of black holes has fascinated scientists at least since Michell and Laplace's proposal that a gravitating object could exist from which light could not escape. In the 20th century, in light of the general theory of…
The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…
In this review I summarise the status of observational research into relativistic jets from X-ray binaries, highlighting four areas in particular: (i) How relativistic are the jets ?, (ii) The disc : jet coupling, (iii) the nature of the…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes…
The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by…
We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as…
Quite recently, some new mathematical approaches to black holes have appeared in the literature. They do not rely on the classical concept of event horizon -- which is very global, but on the local concept of hypersurfaces foliated by…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
Spacetime singularities in numerical relativity can be avoided by excising a region of the computational domain from inside the apparent horizon. We report on results of such a scheme that is based on using ({\it i}) a horizon locking…
This chapter briefly discusses the fundamental properties of black holes in general relativity, the discovery of astrophysical black holes and their main astronomical observations, how X-ray and $\gamma$-ray facilities can study these…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes…