We present two results for bounding marginally outer trapped surfaces (MOTSs) in Killing initial data satisfying the null energy condition and containing an untrapped barrier. The first one applies to the stationary case and states that no bounding MOTS lying in the exterior region where the stationary Killing vector is causal and penetrating into the timelike region can exist. The second result applies to the static case and shows that no bounding MOTS can penetrate into the exterior region where the static Killing vector is timelike. These results extend an interesting theorem by P. Miao (Miao 2005).

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.


The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for some families of black holes and find that the Ruppeiner geometry is flat for Reissner–Nordström black holes in any dimension, while curvature singularities occur for the Kerr black holes. Kerr black holes have instead flat Weinhold curvature.

In this contribution we summarize some of our recent results about the matching of collapsing inhomogeneous dust-filled spacetimes to vacuum static exteriors with a negative cosmological constant in planar or hyperbolic symmetry. This models gravitational collapse to toroidal or higher genus asymptotically AdS black holes.


In this talk we present the latest results from our ongoing project on geometro-thermodynamics (also known as information geometry of thermodynamics or Ruppeiner geometry) of dilaton BHs in 4D in both Einstein and string frames and a dyonic dilaton BH and at the end we report very briefly results from this approach to the 2D dilaton BHs.

We check the feasibility of the Thin-Sandwich formulation of the constraints for the construction of hyperboloidal initial data, and present a first numerical check (boundary treatment) of the method with Schwarzschild data.

We show that the metric f(R) theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is prooved in general terms for all metric theories of gravity which can be expressed as powers of Ricci's scalar R. We also show that an extra additional lensing as compared to that predicted by standard general relativity is produced in that theory.

Nowadays, Gravitational lensing is a fundamental tool to study the light propagation in the universe and the evolution of structures. Here, diferent forms of the Santos & Lima smoothness parameter as a funtion of cosmological redshift are used in order to describe various scenarios of evolution of structure. Its effects on the strong gravitational lensing SGL by galaxy cluster dark halos are analized in LCDM, EdS and OCDM cosmologies. The dark matter halos modeled by Navarro-Frenk-White singular profile and the Preses-Schechter approximation is assumed to describe its distribution. We found that SGL probability by galaxy clusters becomes to be sensible to the evolution of structures scenario considered for sources farther than z ≈ 2 and it strongly depends on the cosmology and the smoothness parameter actual value.

We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. The numerical results also indicate that the vertical oscillation amplifies another waves with odd azimuthal wave-numbers in the horizontal plane like Faraday resonance. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

An unambiguous physical definition of creatable universes was recently proposed. According to it, flat and closed Friedmann-Robertson-Walker (FRW) backgrounds can be created as quantum vacuum fluctuations, whereas open backgrounds are not creatable. Here, physically motivated perturbations of closed and flat backgrounds are analyzed. Various creatable perturbed FRW universes are thus found. Some of them involve scalar and tensor perturbations with appropriate spectra, whereas other ones are Bianchi models.

We show that some types of sudden singularities admit a natural explanation in terms of regular changes of signature on brane-worlds in AdS5. 
The present accelerated expansion of the Universe and its possible ending at a sudden singularity may therefore simply be an indication that our braneworld is about to change its Lorentzian signature to an Euclidean one, while remaining fully regular. An explicit example of this behaviour satisfying the weak and strong energy conditions is presented. 


A new analitycally approximated interior metric for a stationary compact perfect fluid with equation of state µ+(1–n)p = µ0 is presented. Also, it is concluded that an object of this kind can be a source of Wahlquist's metric.

We construct an approximate asymptotically flat stationary and axisymmetric vacuum metric by imposing matching conditions on an interior metric associated to a perfect fluid with equation of state µ+(1–n)p = µ0. A comparison between this vacuum metric and the Kerr one is made. Finally, a brief reflexion about the Wahlquist metric is commented in relation with our results.

It is shown that the cosmological constant problem in brane-world is different from the same problem in general relativity, essentially because the gauge fields fields contributing to the vacuum energy are confined to the brane-world, but the cosmological term propagates in the bulk. The brane-wrld equations of motion include a second order, conserved symmetric tensor field in four dimensions defined by the extrinsic curvature, which adjusts the vacuum energy. In the application to the FRW brane-world universe embedded in a five-dimensional deSitter bulk, that tensor modifies Friedman's equation with a remarkable agreement with the current gold set of cosmological data.

The basic theory on relativistic positioning systems in a two-dimensional space-time and the analysis of the possibility of making relativistic gravimetry with these systems have been presented elsewhere [Phys. Rev. D 73, 084017 (2006); Phys. Rev. D 74, 104003 (2006)]. Here we summarize these results and we outline new issues on the relativistic positioning systems in Minkowski plane. We point out that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters and only during a light echo interval.

Locally 2+2 warped product metrics with a Lorentzian base and Riemannian fiber are described in Newman-Penrose formalism. It is shown that solutions with rank-1 Ricci tensor are characterized by Φ11 + 3Λ = 0 and Φ00Φ22 = (Φ11-3Λ)2. Integrability conditions for the Bianchi identities are studied and it is proved that the sources are null Einstein-Maxwell fields, massless scalar fields or stiff matter fields corresponding respectively to Λ = 0, Λ > 0 or Λ < 0.

The ESA BepiColombo mission, scheduled for launch in 2013 with a two–satellite configuration, will represent an important step in the exploration of the Solar System and will contribute to fundamental physics. Among the main scientific objectives of this mission are the Radio Science Experiments: gravimetry and rotation of Mercury and tests of Einstein's theory of general relativity, to be achieved by the MPO (Mercury Planetary Orbiter) satellite. The ISA (Italian Spring Accelerometer) instrument will give a fundamental contribution to these experiments by providing a continuous measurement of the non–gravitational accelerations acting on the MPO. After a description of the mission, the rôle of the ISA accelerometer will be discussed, together with the current activity for its development.

This paper reports the development of an experiment (TEPEE/GReAT) to test the Equivalence Principle (EP) at a level of accuracy equal to 5 × 10-15, by means of a differential accelerometer free falling in a cryogenic vacuum capsule released from a stratospheric balloon. Such an accuracy requires resolving a very small signal out of the instrument's intrinsic noise and the noise associated with the instrument's motion. Imperfections in the construction of the detector introduce gravity gradient noise that it is possible to separate from the violation signal spinning the detector around an horizontal axis in order to have the EP violation signal and the gravity gradients one modulated at two different frequencies. Experimental results on prototype instruments showing high sensitivity and common mode rejection factor are shown.

We describe a way to compare current relativistic astrometric models accurate to the micro-arcsecond level from which an astrometric catalogue will be deduced. The observed stellar direction can be written as a function of several parts, linking the astrometric observables to the relativistic effects associated to the stellar kinematical properties and distances as seen inside the gravitational field of our Solar System, i.e. the so called relativistic astrometric parameters, providing a tool for comparing the RAMOD framework to the pM/pN approaches.

This paper analyses cosmological observations within inhomogeneous and exact solutions of the Einstein equations. In some way the analyses presented here can be freed from assumptions such as small amplitude of the density contrast. The supernova observations are analysed using the Lemaître–Tolman model and the CMB observations are analysed using the quasispherical Szekeres model. The results show that it is possible to fit the supernova data without the cosmological constant. However if inhomogeneities of sizes and amplitudes as observed in the local Universe are considered, their impact on cosmological observations is small.