Abstract:
The emission spectrum from a simple accretion disk model around a compact object is compared for the cases of a black hole (BH) and a boson star (BS) playing the role of the central object. It was found in the past that such a spectrum presents a hardening at high frequencies; however, here it is shown that the self-interaction and compactness of the BS have the effect of softening the spectrum, the less compact the star is, the softer the emission spectrum at high frequencies. Because the mass of the boson fixes the mass of the star and the self-interaction the compactness of the star, we find that, for certain values of the BS parameters, it is possible to produce similar spectra to those generated when the central object is a BH. This result presents two important implications: (i) using this simple accretion model, a BS can supplant a BH in the role of compact object accreting matter, and (ii) within the assumptions of the present accretion disk model we do not find a prediction that could help distinguish a BH from a BS with appropriate parameters of mass and self-interaction.

Abstract:
The status of boson stars as black hole mimickers is presented. We focus on the analysis of the emission spectrum of a simple accretion disk model. We describe the free parameters that allow a boson star to become a black hole mimicker and present an example of a particular astrophysical case.

Abstract:
In the present paper are analysed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing the scaling properties of the fundamental macroscopic observables in the Thermodynamic Limit. It is shown that the Generalized Legendre Formalism in the Tsallis Statistic only could be applied for one special class of the bordering systems, those with non exponential growth of the accessible states density in the thermodynamic limit and zero-order divergency behavior for the fundamental macroscopic observables, systems located in the chaos threshold.

Abstract:
We discuss different aspects of the present status of the Statistical Physics focusing the attention on the non-extensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric aspects are presented. The same could be a very atractive way to generalize the Thermodynamics. It is suggested that if the Multimicrocanonical Distribution could be equivalent in the Thermodynamic Limit with some generalized Canonical Distribution, then it is possible to estimate the entropic index of the non-extensive thermodynamics of Tsallis without any additional postulates.

Abstract:
Astrophysical systems will never be in a real Thermodynamic equilibrium: they undergo an evaporation process due to the fact that the gravity is not able to confine the particles. Ordinarily, this difficulty is overcome by enclosing the system in a rigid container which avoids the evaporation. We proposed an energetic prescription which is able to confine the particles, leading in this way to an alternative version of the Antonov isothermal model which unifies the well-known isothermal and polytropic profiles. Besides of the main features of the isothermal sphere model: the existence of the gravitational collapse and the energetic region with a negative specific heat, this alternative model has the advantage that the system size naturally appears as a consequence of the particles evaporation.

Abstract:
We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling laws of the thermodynamical variables and potentials in the thermodynamic limit. Geometrical considerations motivate a way by means of which could be carried out a well-defined generalized canonical-like description for this kind of systems, even being nonextensive. This interesting possibility allows us to extend the applicability of the Standard Thermodynamic methods, even in the cases in which the system exhibits a negative specific heat. As example of application, we reconsider the classical Antonov problem of the isothermal spheres.

Abstract:
According to self-similarity hypothesis, the thermodynamic limit could be defined from the scaling laws for the system self-similarity by using the microcanonical ensemble. This analysis for selfgravitating systems yields the following thermodynamic limit: send N to infinity, keeping constant E/N^{(7/3)} and LN^{(1/3)}, in which is ensured the extensivity of the Boltzmann entropy S_{B}=lnW(E,N). It is shown how the consideration of this thermodynamic limit allows us to explain the origin of dynamical anomalies in numerical simulations of selfgravitating systems.

Abstract:
In the present paper are considered the self-similarity scaling postulates in order to extend the Thermodynamics to the study of one special class of nonextensive systems: the pseudoextensive, those with exponential behavior for the asymptotical states density of the microcanonical ensemble. It is shown that this kind of systems could be described with the usual Boltzmann-Gibbs' Distribution with an appropriate selection of the representation of the movement integrals. It is shown that the pseudoextensive systems are the natural frame for the application of the microcanonical thermostatistics theory of D. H. E. Gross.

Abstract:
We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the microcanonical ensemble, but this time, considering its equivalence with some generalized canonical ensemble in the thermodynamic limit by means of the scaling properties of the fundamental physical observables.