We develop a simple method of dark energy reconstruction using a geometrical form of the luminosity-distance relation. In this method the FRW dynamical system with dark energy is reconstructed instead of the equation of state parameter. We give several examples which illustrate the usefulness of our method in fitting the redshift transition from the decelerating to accelerating phase as the value of the Hubble function at the transition.

f(R) gravity is attracting a lot of interest as alternativecandidates to explain the observed cosmic acceleration and themissing matter in large scale structures. Very likely, what wecall “Dark Matter” and “Dark Energy” are nothing else but signalsof the breakdown of General Relativity at large scales. Besides,Solar System experiments do not exclude, a priori, the possibilitythat such theories could give small observable effects also atthese scales. We review some results giving the basic ingredientsof such an approach.

A longstanding problem in braneworld cosmology is quantifying thedynamics of cosmological perturbations. This is because, unlike the4-dimensional case, fluctuations are governed by non-separablepartial differential equations (PDEs). We have developed a fast andaccurate code to solve the relevant equations of motion, and henceextract observational predictions from braneworld models. Here, webriefly review braneworld scenarios, the perturbation problem, ournumerical methods, and the results we have obtained for theRandall-Sundrum (RS) and Dvali-Gabadadze-Porrati (DGP) scenarios.

We examine static spherically symmetric polytropic spheres inPalatini f(R) gravity and show that no regular solutions to thefield equations exist for physically relevant cases such as amonatomic isentropic gas or a degenerate electron gas, thus castingdoubt on the validity of Palatini f(R) gravity as an alternative toGeneral Relativity.

We report on some recent results on a class of relativisticlagrangian field theories supporting non-topological solitonsolutions and their applications in the contexts of Gravitationand Cosmology. We analyze one and many-components scalar fieldsand gauge fields

We include a Chern-Simons term in a GL(3,R) gauge formulation ofgravity with a cosmological contribution in 2+1 dimension and weexplore consistence showing that excitations must be causal andstandard topological massive gravity is recovered from this typeof construction at the torsionless limit.

Global hyperbolicity is a classical and well-known concept, whichlies in the core of General Relativity. Here we discuss brieflyfive approaches to this concept. They yield different definitionswhich become natural in diverse contexts: the initial valueproblem, singularity theorems, existence of maximizing causalgeodesics, possibility to split globally the spacetime, causalboundaries. The neat formulation and definitive equivalencebetween these definitions have been completed only recently. Avery brief summary is presented.

Magnetic fields can be generated during an inflationary phase in the early universeby amplification of perturbations of the electromagnetic field. The resulting magnetic fields can have interesting field strengths if the conformal invariance of Maxwell's equations is broken. Two particular models are discussed, one based on extra dimensions and one on nonlinear electrodynamics.

We provide a covariant derivation of plasma physics coupled to gravitation by utilizing the 3+1 formulation of general relativity, including a discussion of the Lorentz force law. We then reduce the system to the spherically symmetric case and show that all regions of the spacetime can be represented in a single coordinate system, thus revoking the need for junction conditions. We further show that the region exterior to the collapsing region is naturally described by the charged Vaidya spacetime in non-null coordinates.

We present a new numerical dissipation algorithm, which can beefficiently used in combination with centered finite-differencemethods. We start from a formulation of centered finite-volumemethods for Numerical Relativity, in which third-order spaceaccuracy can be obtained by employing just piecewise-linearreconstruction. We obtain a simplified version of the algorithm,which can be viewed as a centered finite-difference method plussome “adaptive dissipation”. The performance of this algorithm isconfirmed by numerical results obtained from 3D black holesimulations.

Applications of Discrete Differential Forms in numerical GR aredescribed. The motivation to use this finite element method isits manifest coordinate independence. It is discussed how numericalschemes based on this method were developed and results ofsimulations for spherically symmetric vacuum space-times are presented.

We report on the systematic listing of polynomial relationsamong the algebraic invariants of a Riemann tensor. We constructall such relations for the 3 × 1029 invariants with upto seven Riemann tensors, and provide the computer algebra systemInvar (both for Mathematica and Maple)which uses them to maximally simplify any invariant within seconds.We also report work in progress to extend Invarand its database to handle all differential Riemann invariants upto 12 derivatives of the metric.

In the dense central regions of globular clusters close encounters oftwo white dwarfs are relatively frequent (one or more strongencounters per star in the lifetime of the cluster). Such encountersshould be potential sources of gravitational wave emission. Thus, itis foreseeable that these collisions could be either detected by LISAor they could contribute significantly to the background noise of thedetectors. We compute the gravitational wave pattern resulting fromthese encounters for a broad range of system parameters, which includethe masses and the relative distances of the white dwarfs involved inthe encounter.

In this work the full orthogonal splitting of Bel andBel-Robinson tensors in a four dimensional spacetime is calculated. We also present the orthogonal splitting of the covariant divergence of Bel-Robinson tensor in vacuum and use the resulting expressions (dynamical laws of superenergy in vacuum) to introduce the concept of intrinsic superenergy radiative state. It is hoped that these results will contribute to the long-standing question of the physical interpretation of the Bel and the Bel-Robinson tensors. 


An invariant classification scheme of algebraicallygeneral rotating dust with a purely electric Weyl tensor ispresented. It turns out that the vorticity vector of the dustcongruence is necessarily parallel to a Weyl principal vector, whichis moreover geodesic. An explicit metric expression can be obtainedfor the subclass of expanding models with one functionallyindependent zero-order Riemann invariant. The basic equations forthe general case, where there are two such invariants, are givenwithin a weighted 1+1+2 tetrad formalism.

We discuss shear-free perfect fluids which obey a barotropic equation of state and for which the magnetic part of the Weyl tensor with respect to the fluid congruence is divergence-free. We show that for a large class of equations of state these fluids are either non-expanding or non-rotating and we present a classification of the resulting non-expanding solutions.

Although the Lanczos potential (a (2,1) form, Labc) for theWeyl tensor does not exist in dimensions greater than four, a newpotential (a (2,3) form, Pabcde, which coincides with thedouble dual of Labc in four dimensions) has recently beenshown to exist in all dimensions n ≥ 4.In this talk we investigate the question of gauge and discuss the structure of the new potential's wave equation whichis obtained from the Bianchi identities; identifying the gauge supplies us with a new direct proof of the existence of Pabcde via the Cauchy-Kowaleski theorem, as well as the foundation for more general investigations of the first order symmetric hyperbolic structure.

Pullback of CYK tensors to a submanifold is used to construct all solutions ofa CYK equation in anti-de Sitter spacetime.

We attempt to point out the relation between Killing-Yano tensors and non-standard supersymmetries. The Killing-Yano tensors play an important role in the Dirac theory on curved spaces where they produce Dirac-type operators. The Euclidean Taub-NUT space is taken to illustrate some of the aspects of the general discussion about the connection between spacetime higher order geometrical symmetries and supersymmetries.The dynamical symmetry of this space leads in a natural way to an infinite dimensional twisted loop superalgebra of the conserved operators.

Our current picture of black hole gravitational collapserelies on two assumptions: i) the resultingsingularity is hidden behind an event horizon– weak cosmic censorship conjecture – and ii) spacetimeeventually settles down to a stationarity state.In this setting,it follows that the minimal area containing an apparent horizonis bound by the square of the total ADM mass (Penrose inequality conjecture).Following Dain et al. (2002), we construct numerically a familyof axisymmetric initial data with one or several marginallytrapped surfaces. Penrose and related geometric inequalitiesare discused for these data. As a by-product, it is shownhow Penrose inequality can be usedas a diagnosis for an apparent horizon finder numerical routine.