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Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…

This is a new review article for The Review of Particle Physics 2004 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at the end of 2003. Topics included are Parametrizing the Universe;…

Numerical relativity has come a long way in the last three decades and is now reaching a state of maturity. We are gaining a deeper understanding of the fundamental theoretical issues related to the field, from the well posedness of the…

In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate…

A satisfactory formulation of the laws of physics entails that the future evolution of a physical system should be determined from appropriate initial conditions. The existence of Cauchy horizons in solutions of the Einstein field equations…

Shortly the vacuum component of the Universe from the geometry point of view and from the point of view of the standard model of physics of elementary particles is discussed. Some arguments are given to the calculated value of the…

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant…

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein-Gordon) field in three dimensions. The quantization of this latter system…

Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$…

Unimodular relativity is a theory of gravity and space-time with a fixed absolute space-time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an…

Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this…

Focusing on gauge degrees of freedom specified by a 1+3 dimensions model hosting a Maxwell term plus a Lorentz and CPT non-invariant Chern-Simons-like contribution, we obtain a minimal extension of such a system to a supersymmetric…

Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In…

Two ways to deduce the equivalence of the field equations of general relativity and the principle of maximum force $c^4/4G$ - or the equivalent maximum power $c^5/4G$ - are presented. A simple deduction of inverse square gravity directly…

We discuss the case of massive gravitons and their relation with the cosmological constant, considered as an eigenvalue of a Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study…

In a 2013 paper, the author showed that the convolution of a compactly supported measure on the real line with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). In a 2014 paper, the author gave bounds for the optimal…

Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditions for integrability in the Liouville sense for this class…

This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and…

We study the condition that the theory is unitary and stable in three-dimensional gravity with most general quadratic curvature, Lorentz-Chern-Simons and cosmological terms. We provide the complete classification of the unitary theories…

The possible time variation of dimensionless fundamental constants of nature, such as the fine-structure constant $\alpha$, is a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants, such as…