Context. An important aim of standard relativistic cosmology is the empirical verification of its geometrical concept of homogeneity by considering various definitions of distance and astronomical observations occurring along the past light cone. Aims. We analyze the physical consequences of distinguishing between spatial homogeneity (SH), defined by the Cosmological Principle, and observational homogeneity (OH). We argue that OH is falsifiable by means of astronomical observations, whereas SH can be verified only indirectly. Methods. We simulate observational counts of cosmological sources, such as galaxies, by means of a generalized number-distance expression that can be specialized to produce either the counts of the Einstein-de Sitter (EdS) cosmology, which has SH by construction, or other types of counts, which do, or do not, have OH by construction. Expressions for observational volumes are derived using the various cosmological-distance definitions in the EdS cosmological model. The observational volumes and simulated counts are then used to derive differential densities. We present the behavior of these densities for increasing redshift values. Results. Simulated counts that have OH by construction do not always exhibit SH features. The reverse situation is also true. In addition, simulated counts with no OH features at low redshift begin to show OH characteristics at high redshift. The comoving distance appears to be the only distance definition for which both SH and OH are applicable simultaneously, even though with limitations. Conclusions. We demonstrate that observations indicative of a possible absence of OH do not necessarily falsify the standard Friedmannian cosmology, which implies that this cosmology does not always produce observable homogeneous densities. We conclude that using different cosmological distances in the characterization of the galaxy distribution can produce significant ambiguities in reaching conclusions about the large-scale galaxy distribution in the Universe.

We report some recent developments in the understanding of GRBs based on the theoretical framework of the "fireshell" model, already presented in the last three editions of the "Brazilian School of Cosmology and Gravitation". After recalling the basic features of the "fireshell model", we emphasize the following novel results: 1) the interpretation of the X-ray flares in GRB afterglows as due to the interaction of the optically thin fireshell with isolated clouds in the CircumBurst Medium (CBM); 2) an interpretation as "fake -disguised" short GRBs of the GRBs belonging to the class identified by Norris & Bonnell; we present two prototypes, GRB 970228 and GRB 060614; both these cases are consistent with an origin from the final coalescence of a binary system in the halo of their host galaxies with particularly low CBM density n cbm ∼ 10 −3 particles/cm 3 ; 3) the first attempt to study a genuine short GRB with the analysis of GRB 050509B, that reveals indeed still an open question; 4) the interpretation of the GRB-SN association in the case of GRB 060218 via the "induced gravitational collapse" process; 5) a first attempt to understand the nature of the "Amati relation", a phenomenological correlation between the isotropic-equivalent radiated energy of the prompt emission E iso with the cosmological rest-frame νF ν spectrum peak energy E p,i . In addition, recent progress on the thermalization of the electron-positron plasma close to their formation phase, as well as the structure of the electrodynamics of Kerr-Newman Black Holes are presented. An outlook for possible explanation of high-energy phenomena in GRBs to be expected from the AGILE and the Fermi satellites are discussed. As an example of high energy process, the work by Enrico Fermi dealing with ultrarelativistic collisions is examined. It is clear that all the GRB physics points to the existence of overcritical electrodynamical fields. In this sense we present some progresses on a unified approach to heavy nuclei and neutron stars cores, which leads to the existence of overcritical fields under the neutron star crust.1 Part I, Part II and Part III of these Lecture notes have been published respectively in COSMOLOGY AND GRAVITATION: ]. The outcome of this analysis points to the existence of a "canonical" GRB, originating from a variety of different initial astrophysical scenarios. The communality of these GRBs appears to be that they all are emitted in the process of formation of a black hole with a negligible value of its angular momentum. The following sequence of events appears to be canonical: the gravitational collapse to a black hole, the vacuum polarization process in the dyadosphere with the creation of the optically thick self accelerating electron-positron plasma; the engulfment of baryonic mass during the plasma expansion; adiabatic expansion of the optically thick "fireshell" of electron-positronbaryon plasma up to the transparency; the interaction of the accelerated baryonic matter with the CircumBurst Medium (CBM). This leads to the canoni...

We propose a possible explanation, in the context of the Fireshell scenario, for the high-energy emission observed in GRB 080916C and GRB 090902B. The physical process underlying this emission consists mainly in the interaction of the baryon in the Fireshell with some high-density region around the burst site. Moreover we associate the observed delay of the onset of the high-energy emission as due to the P-GRB emission

Pseudoacoustic algorithms are very fast in comparison with full elastic ones for vertical transversely isotropic (VTI) modeling, so they are suitable for many applications, especially reverse time migration. Finite differences using simple grids are commonly used to solve pseudoacoustic equations. We have developed and implemented general high-order 3D pseudoacoustic transversely isotropic formulations. The focus is the development of staggered-grid finite-difference algorithms, known for their superior numerical properties. The staggered-grid schemes based on first-order velocity-stress wave equations are developed in detail as well as schemes based on direct application to second-order stress equations. This last case uses the recently presented equivalent staggered-grid theory, resulting in a staggered-grid scheme that overcomes the problem of large memory requirement. Two examples are presented: a 3D simulation and a prestack reverse time migration application, and we perform a numerical analysis regarding computational cost and precision. The errors of the new schemes are smaller than the existing nonstaggered-grid schemes. In comparison with existing staggered-grid schemes, they require 25% less memory and only have slightly greater computational cost.

Over the last few years, several vibration isolation projects for gravitational wave detectors have been proposed. Some of them are related to N-stages cascaded systems which can achieve great factors of attenuation. However, these systems are usually very tall, which makes it difficult to build an efficient vaccum chamber for them. For this reason, this paper makes a comparison between a theoretical N-stage cascaded pendula with an experimental N-stage nested one. Preliminary results show that their resonant modes are very similar. The ratio between the results of experiment and theory is between 0.94 and 1.01 for the pendular modes and systematically close to 1.05 for the rotational modes. This result implies that an N-stage nested pendula set of about 1.4 m height can have resonant modes similar to a cascaded pendula set of about 6.6 m, which may suggests that a nested system can be theoretically treated as a cascaded one. So, the development of nested pendula can be an effective alternative of vibration isolation systems for future generations of gravitational wave detectors.