The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical reduction to a f
inite ideal gas. In the limit where the thermofractal has no internal structure, it is found that it reproduces the basic properties of a nonextensive ideal gas with a finite number of particles as recently discussed (Lima & Deppman, Phys. Rev. E 101, 040102(R) 2020). In particular, the entropic $q$-index is calculated in terms of the number of particles both for the nonrelativistic and relativistic cases. In light of such results, the possible nonadditivity or additivity of the entropic structures are also critically analysed and new expressions to the entropy (per particle) for a composed system of thermofractals and its limiting case are derived.
A century after observing the deflection of light emitted by distant stars during the solar eclipse of 1919, it is interesting to know the concepts emerged from the experiment and the theoretical and observational consequences for modern cosmology an
d astrophysics. In addition to confirming Einsteins gravitational theory, its greatest legacy was the construction of a new research area to cosmos science dubbed gravitational lensing. The formation and magnification of multiple images (mirages) by the gravitational field of a compact or extended lens are among the most striking phenomena of nature. This article presents a pedagogical view of the first genuine gravitational lens effect, the double quasar QSO 0957 + 561. We also describe the formation of rings, giant arcs, arclets and multiple Supernova images. It is also surprising that the Hubble constant and the amount of dark matter in the Universe can be measured by the same technique. Finally, the lensing of gravitational waves, a possible but still not yet detected effect, is also briefly discussed.
Wong et al. (2018) recently performed an encouraging criticism to our paper Gravitational waves from ultra-short period exoplanets (Cunha, Silva, Lima 2018) exploring the potentialities of a subset of exoplanets with extremely short periods (less tha
n 80 min) as a possible scientific target to the planned space-based LISA observatory. Here we call attention to some subtleties and limitations underlying the basic criticism which in our view were not properly stressed in their comment. Particularly, simple estimates show that a sphere encircling the Earth with a radius of 250 pc may accommodate a population $ sim 10^{4}$ ultra-short period exoplanets with characteristic strain of the same order or higher than the ones analyzed in our paper. This means that the question related to the gravitational wave pattern of ultra-short period exoplanets may be surpassed near future by the LISA instrument with new and more definitive data.
In the last two decades, thousands of extrasolar planets were discovered based on different observational techniques, and their number must increase substantially in virtue of the ongoing and near-future approved missions and facilities. It is shown
that interesting signatures of binary systems from nearby exoplanets and their parent stars can also be obtained measuring the pattern of gravitational waves that will be made available by the new generation of detectors including the space-based LISA (Laser Interferometer Space Antenna) observatory. As an example, a subset of exoplanets with extremely short periods (less than 80 min) is discussed. All of them have gravitational luminosity, $L_{GW} sim 10^{30}$ $erg/s$, strain $h sim 10^{-22}$, frequencies $f_{gw} > 10^{-4}$Hz, and, as such, are within the standard sensitivity curve of LISA. Our analysis suggests that the emitted gravitational wave pattern may also provide an efficient tool to discover ultra short period exoplanets.
The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of t
he Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.
We are experiencing a period of extreme intellectual effervescence in the area of cosmology. A huge volume of observational data in unprecedented quantity and quality and a more consistent theoretical framework propelled cosmology to an era of precis
ion, turning the discipline into a cutting-edge area of contemporary science. Observations with type Ia Supernovae (SNe Ia), showed that the expanding Universe is accelerating, an unexplained fact in the traditional decelerated model. Identifying the cause of this acceleration is the most fundamental problem in the area. As in the scientific renaissance, the solution will guide the course of the discipline in the near future and the possible answers (whether dark energy, some extension of general relativity or a still unknown mechanism) should also leverage the development of physics. In this context, without giving up a pedagogical approach, we present an overview of both the main theoretical results and the most significant observational discoveries of cosmology in the last 100 years. The saga of cosmology will be presented in a trilogy. In this article (Part I), based on the articles by Einstein, de Sitter, Friedmann, Lema^itre and Hubble, we will describe the period between the origins of cosmology and the discovery of Universal expansion (1929). In Part II, we will see the period from 1930 to 1997, closing with the old standard decelerated model. The Part III will be entirely devoted to the accelerated model of the universe, the cosmic paradigm of the XXI century.
The motion of a point like object of mass $M$ passing through the background potential of massive collisionless particles ($m << M$) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian vel
ocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass $M$. In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the $q$-nonextensive kinetic theory. In the extensive limiting case ($q = 1$), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical $N$-body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive $q$-parameter.
The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $Lambda (H) propto H^{n+2}$, is discussed in detail. Specifical
ly, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $rho_r propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of the comoving radiation entropy density (associated to effectively massless particles) starts from zero and evolves extremely fast until reaching a maximum near the end of the vacuum decay phase, where it saturates. The late time conservation of the radiation entropy during the adiabatic FRW phase also guarantees that the whole class of running vacuum models predicts thesame correct value of the present day entropy, $S_{0} sim 10^{87-88}$ (in natural units), independently of the initial conditions. In addition, by assuming Gibbons-Hawking temperature as an initial condition, we find that the ratio between the late time and primordial vacuum energy densities is in agreement with naive estimates from quantum field theory, namely, $rho_{Lambda 0}/rho_{Lambda I} sim10^{-123}$. Such results are independent on the power $n$ and suggests that the observed Universe may evolve smoothly between two extreme, unstable, nonsingular de Sitter phases.
We show that a cosmology driven by gravitationally induced particle production of all non-relativistic species existing in the present Universe mimics exactly the observed flat accelerating $Lambda$CDM cosmology with just one dynamical free parameter
. This kind of scenario includes the creation cold dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a particular case and also provides a natural reduction of the dark sector since the vacuum component is not needed to accelerate the Universe. The new cosmic scenario is equivalent to $Lambda$CDM both at the background and perturbative levels and the associated creation process is also in agreement with the universality of the gravitational interaction and equivalence principle. Implicitly, it also suggests that the present day astronomical observations cannot be considered the ultimate proof of cosmic vacuum effects in the evolved Universe because $Lambda$CDM may be only an effective cosmology.
Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are capable to solve or at least to alleviate some cosmological puzzles, among them: (i) the singularity, (ii) horizon, (iii) gracef
ul-exit from inflation, and (iv) the baryogenesis problem. Our basic aim here is to discuss how the coincidence problem based on a large class of running vacuum cosmologies evolving from de Sitter to de Sitter can also be mollified. It is also argued that even the cosmological constant problem become less severe provided that the characteristic scales of the two limiting de Sitter manifolds are predicted from first principles.
