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The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match…
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and…
The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
The current standard model of cosmology, the LambdaCDM model, is based on the homogeneous FLRW solutions of the Einstein equations to which some perturbations are added to account for the CMB features and structure formation at large…
The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess a very unphysical property. Specifically, in this model some trajectories are discontinuous functions of their initial…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
Accounting for large-scale structure in our universe will require not only reasonably accurate mathematical models of its cosmogony, topology and cosmology, but also a more deeper understanding of our fundamental physical concepts of space,…
I give a brief and elementary introduction to braneworld models with large extra dimensions. Three conceptually distinct scenarios are outlined: (i) Large compact extra dimensions; (ii) Warped extra dimensions; (iii) Infinite-volume extra…
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark…
Unimodular gravity provides a theoretical framework that allows for non-conservation of energy-momentum, with possible implications for the cosmological constant problem. It is then important to study the predictions of unimodular gravity…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
Cosmologies including continuous matter creation are able to reproduce the main properties of the standard $\Lambda$CDM model, in particular in cases where the particle and entropy production rates are equal. These specific models,…
The prospects of measuring masses, spin and CP properties within Supersymmetry and other beyond the Standard Model extensions at the LHC are reviewed. Emphasis is put on models with missing transverse energy due to undetected particles, as…
As previously observed the massless limit of massive gravity leads to a modification of general relativity. Here we study spherically symmetric solutions of the modified field equations which contain normal matter together with a dark…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
We introduce a procedure to determine the size and shape of normal neighborhoods in any spacetimes and their dependence on the precision of the measurements performed by arbitrary observers. As an example, we consider the Schwarzschild…
The recently suggested notion of total mass density for closed universes is extended to closed universes with a positive cosmological constant. Assuming that the matter fields satisfy the dominant energy condition, it is shown that the…
We present spherically symmetric solutions to Einstein's equations which are equivalent to canonical Schwarzschild and Reissner-Nordstrom black holes on the exterior, but with singular (Planck-density) shells at their respective event and…