arXiv subjects

Marcelo B. Ribeiro

Publications and source records attributed to Marcelo B. Ribeiro.

At least 19 recordsLinked to original sources

arXiv2026

Shift vector sign reversal in the Alcubierre warp drive spacetime geometry and nonlinear Burgers-type dynamics

This work investigates a sign reversal of the shift vector in the Alcubierre Warp Drive geometry and its effect on the nonlinear reduced structure of the Einstein equations. Previous analyses showed that Burgers-type equations can arise in warp drive spacetimes, leading to vacuum solutions under suitable assumptions on the sign of the shift vector and on matter-source reductions. Here, we analyze the original Alcubierre shift-vector sector and show that, under an appropriate mathematical ansatz, the $\{22\}$ and $\{33\}$ components of the Einstein equations can be formally decomposed into viscous Burgers-type and heat-type equations. The resulting heat-type structure and the constant analogous to a diffusivity coefficient constitute new formal features of the reduced shift-vector dynamics. Since these terms are introduced through an ansatz and are not generated by a specific energy-momentum tensor source, they should not be interpreted as physical diffusivity without an additional matter model. The vacuum reductions of the Einstein equations for the warp-drive geometry come with an important caveat: the shift vector must depend only on time and on one spatial coordinate, namely $β(t,x)$. Consequently, the Alcubierre regulating function no longer retains its original spherical dependence on $r_s(t)$, and the resulting solutions should be interpreted as lower-dimensional shift-sector reductions rather than complete spherically symmetric warp bubble configurations.

gr-qc↗

arXiv2026

Fractal dimension of the cosmic web with different galaxy types

The fractal dimension $D$ is used to map the large-scale galaxy distribution in the Universe by color types: blue, green and red. Using a $NUVrK$-complete COSMOS2020 subsample of 618,952 galaxies observed up to $z=4$, number densities were derived and plotted against two cosmological distance measures, the luminosity and comoving (galaxy area) distances, in order to estimate $D$ for each galaxy color type in two redshift intervals: $z\gtrless1$. We found a general gradient $D_{\mathrm{blue}}> D_{\mathrm{red}}>D_{\mathrm{green}}$ with $D=1.40-2.03$ for $z<1$. For $1 D_{\mathrm{green}}>D_{\mathrm{red}}$, and the fractal dimension values are lower, $D=0.03-0.44$. These results suggest that the fractal dimension is a sensitive diagnostic for how galaxy populations trace the evolving cosmic web, and confirm the fractal dimension as a useful tool for observational mapping of large-scale structure by galaxy color.

astro-ph.CO↗

arXiv2025

Matching the Alcubierre and Minkowski spacetimes

This work analyzes the Darmois junction conditions matching an interior Alcubierre warp drive spacetime to an exterior Minkowski geometry. The joining hypersurface requires that the shift vector of the warp drive spacetime must satisfy the solution of a particular inviscid Burgers equation, namely, the gauge where the shift vector is not a function of the $y$ and $z$ spacetime coordinates. Such a gauge connects the warp drive metric to shock waves via a Burgers-type equation, which was previously found to be an Einstein equations vacuum solution for the warp drive geometry. It is also shown that not all Ricci and Riemann tensors components are zero at the joining hypersurface, but for that to happen they depend on the shift vector solution of the inviscid Burgers equation at the joining wall. This means that the warp drive geometry is not globally flat.

gr-qc↗

arXiv2025

World personal income distribution evolution measured by purchasing power parity exchange rates

The evolution of global income distribution from 1988 to 2018 is analyzed using purchasing power parity exchange rates and well-established statistical distributions. This research proposes the use of two separate distributions to more accurately represent the overall data, rather than relying on a single distribution. The global income distribution was fitted to log-normal and gamma functions, which are standard tools in econophysics. Despite limitations in data completeness during the early years, the available information covered the vast majority of the world's population. Probability density function (PDF) curves enabled the identification of key peaks in the distribution, while complementary cumulative distribution function (CCDF) curves highlighted general trends in inequality. Initially, the global income distribution exhibited a bimodal pattern; however, the growth of middle classes in highly populated countries such as China and India has driven the transition to a unimodal distribution in recent years. While single-function fits with gamma or log-normal distributions provided reasonable accuracy, the bimodal approach constructed as a sum of log-normal distributions yielded near-perfect fits.

econ.GN↗

arXiv2025

Modeling Income Distribution with the Gause-Witt Population Ecology System

This paper presents an empirical application of the Gause-Witt model of population ecology and ecosystems to the income distribution competitive dynamics of social classes in economic systems. The Gause-Witt mathematical system of coupled nonlinear first-order ordinary differential equations employed to model population of species sharing the same ecological niche and competing for the same resources was applied to the income data of Brazil. Previous studies using Brazilian income data from 1981 to 2009 showed that the complementary cumulative distribution functions built from yearly datasets have two distinct segments: the lower income region comprising of about 99% of the population can be represented by the Gompertz curve, whereas the richest 1% is described by the Pareto power-law. The results of applying the Gause-Witt system to Brazilian income data in order to describe the distributive competition dynamics of these two population shares indicate that the 99% and 1% income classes are mostly in the dynamic state of stable coexistence.

physics.soc-ph↗

arXiv2025

Galaxy Mergers in a Fractal Cosmology

This work discusses the influence of galaxy mergers in the evolution of a parabolic Lema\^ıtre-Tolman-Bondi (LTB) cosmology with simultaneous big bang endowed with two consecutive single fractal galaxy distributions systems possessing fractal dimension $D$. Based on recent empirical findings, it is assumed that the resulting galaxy mass from mergers can be expressed by a redshift dependent decaying power law. The proposed cosmological model modifies the relativistic fractal number counts distribution by including a merger rate evolution that estimates the model's radial density. Numerical solutions for the first order small-merger-rate approximation (SMRA) are found and the results show that a fractal galaxy distribution having $D=1.5$ in the range $0.1<z<1.0$, and $D=0.5$ for $1<z<6$, as suggested by recent empirical findings, the SMRA allows consistent description of the model for a merger rate power law exponent up to $q=0.2$ considering a fractal galaxy distribution starting from the Local Group. Consistent values were also found up to $q=2.5$ and $z=7$ from a scale smaller than the Local Supercluster. These results show that galaxy mergers can be successfully incorporated into the dynamics of a parabolic LTB fractal cosmology.

astro-ph.CO↗

arXiv2022

Galaxy Distributions as Fractal Systems

This paper discusses if large scale galaxy distribution samples containing almost one million objects can be characterized as fractal systems. The analysis performed by Teles et al. (2021; arXiv:2012.07164) on the UltraVISTA DR1 survey is extended here to the SPLASH and COSMOS2015 catalogs, hence adding 750k new galaxies with measured redshifts to the studied samples. The standard $Λ$CDM cosmology having $H_0=(70\pm5)$ km/s/Mpc and number density tools required for describing these galaxy distributions as single fractal systems with dimension $D$ are adopted. We use the luminosity distance $d_L$, redshift distance $d_z$ and galaxy area distance (transverse comoving distance) $d_G$ as relativistic distance definitions to derive galaxy number densities in the redshift interval $0.1\le z\le4$ at volume limited subsamples defined by absolute magnitudes in the K-band. Similar to the findings of Teles et al. (2021; arXiv:2012.07164), the results show two consecutive redshift scales where galaxy distribution data behave as single fractal structures. For $z<1$ we found $D=1.00\pm0.12$ for the SPLASH galaxies, and $D=1,39\pm0.19$ for the COSMOS2015. For $1\le z\le4$ we respectively found $D=0.83^{+0.36}_{-0.37}$ and $D=0.54^{+0.27}_{-0.26}$. These results were verified to be robust under the assumed Hubble constant uncertainty. Calculations considering blue and red galaxies subsamples in both surveys showed that the fractal dimensions of blue galaxies as basically unchanged, but the ones for the red galaxies changed mostly to smaller values, meaning that $D$ may be seen as a more intrinsic property of the distribution of objects in the Universe, therefore allowing for the fractal dimension to be used as a tool to study different populations of galaxies. All results confirm the decades old theoretical prediction of a decrease in the fractal dimension for $z>1$.

astro-ph.CO↗

arXiv2022

The Power Spectrum of Cosmological Number Densities

We study the cosmological power spectra (PS) of the differential and integral galaxy volume number densities $γ_i$ and $γ_i^{*}$, constructed with the cosmological distances $d_i$ $(i=A,G,L,Z)$, where $d_A$ is the angular diameter distance, $d_G$ is the galaxy area distance, $d_L$ is the luminosity distance and $d_z$ is the redshift distance. Theoretical and observational quantities were obtained in the FLRW spacetime with a non-vanishing $Λ$. The radial correlation $Ξ_i$, as defined in the context of these densities, is discussed in the wave number domain. All observational quantities were computed using luminosity function (LF) data obtained from the FORS Deep Field galaxy survey. The theoretical and observational PS of $γ_i$, $γ_i^{\ast}$, $Ξ_i$ and $γ_i / γ_i^\ast$ were calculated by performing Fourier transforms on these densities previously derived by Iribarrem et al. (2012) from the observed values $γ_{obs}$ and ${γ^\ast}_{obs}$ obtained using the galactic absolute magnitudes and galaxy LF Schechter's parameters presented in Gabasch et al. (2004, 2006) in the range $0.5 \le z \le5.0$. The results show similar behavior of the PS obtained from $γ$ and $γ^{\ast}$ using $d_L$, $d_z$ and $d_G$ as distance measures. The PS of the densities defined with $d_A$ have a different and inconclusive behavior, as this cosmological distance reaches a maximum at $z\approx 1.6$ in the adopted cosmology. For the other distances, our results suggest that the PS of ${γ_i}_{obs}$, ${γ^\ast_i}_{obs}$ and ${γ_i / γ^{\ast}_i}_{obs}$ have a general behavior approximately similar to the PS obtained with the galaxy two-point correlation function and, by being sample size independent, they may be considered as alternative analytical tools to study the galaxy distribution.

astro-ph.CO↗

arXiv2021

Warp drive dynamic solutions considering different fluid sources

Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks. Although initial results indicated this scenario as being unphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such an unphysical situation may not always be necessarily true. In this paper we review some solutions of the Einstein equations using the original Alcubierre warp drive metric endowed with various matter-energy sources, namely dust, perfect fluid, anisotropic fluid, and perfect fluid with a cosmological constant. A connection of some of these solutions featuring shock waves described by the Burgers equation is also shown.

gr-qc↗

arXiv2021

Perfect fluid warp drive solutions with the cosmological constant

The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities. In this work we advance solutions of the Einstein equations with the cosmological constant for the Alcubierre warp drive metric having the perfect fluid as source. We also consider the particular dust case with the cosmological constant, which generalizes our previous dust solution (arXiv:2008.06560) and led to vacuum solutions connecting the warp drive with shock waves via the Burgers equation, as well as our perfect fluid solution without the cosmological constant (arXiv:2101.11467). All energy conditions are also analyzed. The results show that the shift vector in the direction of the warp bubble motion creates a coupling in the Einstein equations that requires off-diagonal terms in the energy-momentum source. Therefore, it seems that to achieve superluminal speeds by means of the Alcubierre warp drive spacetime geometry one may require a complex configuration and distribution of energy, matter and momentum as source in order to produce a warp drive bubble. In addition, warp speeds seem to require more complex forms of matter than dust for stable solutions and that negative matter may not be a strict requirement to achieve global superluminal speeds.

gr-qc↗

arXiv2021

Charged dust solutions for the warp drive spacetime

The Alcubierre warp drive metric is a spacetime construction where a massive particle located inside a spacetime distortion, called warp bubble, travels at velocities arbitrarily higher than the velocity of light. This theoretically constructed spacetime geometry is a consequence of general relativity where global superluminal velocities, also known as warp speeds, are possible, whereas local speeds are limited to subluminal ones as required by special relativity. In this work we analyze the solutions of the Einstein equations having charged dust energy-momentum tensor as source for warp velocities. The Einstein equations with the cosmological constant are written and all solutions having energy-momentum tensor components for electromagnetic fields generated by charged dust are presented, as well as the respective energy conditions. The results show an interplay between the energy conditions and the electromagnetic field such that in some cases the former can be satisfied by both positive and negative matter density. In other cases the dominant and null energy conditions are violated. A result connecting the electric energy density with the cosmological constant is also presented, as well as the effects of the electromagnetic field on the bubble dynamics.

gr-qc↗

arXiv2021

Fluid dynamics in the warp drive spacetime geometry

The Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called warp bubble, where a massive particle inside it acquires global superluminal velocities, or warp speeds. This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. The energy-momentum tensor considered two fluid contents, the perfect fluid and the parametrized perfect fluid (PPF), a tentative more flexible model whose aim is to explore the possibilities of warp drive solutions with positive matter density content. Santos-Pereira et al. (2020; arXiv:2008.06560) have already showed that the Alcubierre metric having dust as source connects this geometry to the Burgers equation, which describes shock waves moving through an inviscid fluid, but led the solutions back to vacuum. The same happened for two out of four solutions subcases for the perfect fluid. Other solutions for the perfect fluid indicate the possibility of warp drive with positive matter density, but at the cost of a complex solution for the warp drive regulating function. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. Weak, dominant, strong and null energy conditions were calculated for all studied subcases, being satisfied for the perfect fluid and creating constraints in the PPF quantities such that positive matter density is also possible for creating a warp bubble. Summing up all results,energy-momentum tensors describing more complex forms of matter, or field, distributions generate solutions for the Einstein equations with the warp drive metric where negative matter density might not be a strict precondition for attaining warp speeds.

gr-qc↗

arXiv2020

Fractal Analysis of the UltraVISTA Galaxy Survey

This paper seeks to test if the large-scale galaxy distribution can be characterized as a fractal system. Tools appropriate for describing galaxy fractal structures with a single fractal dimension $D$ in relativistic settings are developed and applied to the UltraVISTA galaxy survey. A graph of volume-limited samples corresponding to the redshift limits in each redshift bins for absolute magnitude is presented. Fractal analysis using the standard $Λ$CDM cosmological model is applied to a reduced subsample in the range $0.1\le z \le 4$, and the entire sample within $0.1\le z\le 6$. Three relativistic distances are used, the luminosity distance $d_L$, redshift distance $d_z$ and galaxy area distance $d_G$, because for data at $z\gtrsim 0.3$ relativistic effects are such that for the same $z$ these distance definitions yield different values. The results show two consecutive and distinct redshift ranges in both the reduced and complete samples where the data behave as a single fractal galaxy structure. For the reduced subsample we found that the fractal dimension is $D=\left(1.58\pm0.20\right)$ for $z<1$, and $D=\left(0.59\pm0.28\right)$ for $1\le z\le 4$. The complete sample yielded $D=\left(1.63\pm0.20\right)$ for $z<1$ and $D=\left(0.52\pm0.29\right)$ for $1\le z\le6$. These results are consistent with those found by Conde-Saavedra et al. (2015; arXiv:1409.5409v1), where a similar analysis was applied to a much more limited survey at equivalent redshift depths, and suggest that either there are yet unclear observational biases causing such decrease in the fractal dimension, or the galaxy clustering was possibly more sparse and the universe void dominated in a not too distant past.

astro-ph.CO↗

arXiv2020

Dust content solutions for the Alcubierre warp drive spacetime

The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This is a consequence of general relativity, which allows global superluminal velocities but restricts local speeds to subluminal ones as required by special relativity. In this work we solved the Einstein equations for the Alcubierre warp drive spacetime geometry considering the dust matter distribution as source, since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as a spacetime geometry proposed without a source gravity field. We found out that all Einstein equations solutions of this geometry containing pressureless dust lead to vacuum solutions. We also concluded that these solutions connect the Alcubierre metric to the Burgers equation, which describes shock waves moving through an inviscid fluid. Our results also indicated that these shock waves behave as plane waves.

gr-qc↗

arXiv2020

High-derivatives and massive electromagnetic models in the Lemaitre-Tolman-Bondi spacetime

The Maxwell electromagnetic theory embedded in an inhomogeneous Lema\^ıtre-Tolman-Bondi (LTB) spacetime background was described a few years back in the literature. However, terms concerning the mass or high-derivatives were no explored. In this work we studied the inhomogeneous spacetime effects on high-derivatives and massive electromagnetic models. We used the LTB metric and calculated the physical quantities of interest, namely the scale factor, density of the electromagnetic field and Hubble constant, for the Proca and higher-derivative Podolsky models. We found a new singularity in both models, and that the magnetic field must be zero in the Proca model.

gr-qc↗

arXiv2019

Oscillations in the Tsallis income distribution

Oscillations in the complementary cumulative distribution function (CCDF) of individual income data have been found in the data of various countries studied by different authors at different time periods, but the dynamical origins of this behavior are currently unknown. Although these datasets can be fitted by different functions at different income ranges, the Tsallis distribution has recently been found capable of fitting the whole distribution by means of only two parameters. This procedure showed clearly such oscillatory feature in the entire income range feature, but made it particularly visible at the tail of the distribution. Although log-periodic functions fitted to the data are capable of describing this behavior, a different approach to naturally disclose such oscillatory characteristics is to allow the Tsallis $q$-parameter to become complex. In this paper we use this idea in order to describe the behavior of the CCDF of the Brazilian personal income recently studied empirically by Soares et al.\ (2016). Typical elements of periodic motion, such as amplitude and angular frequency coupled to this income analysis, were obtained by means of this approach. A highly non-linear function for the CCDF was obtained through this methodology and a numerical test showed it capable of recovering the main oscillatory feature of the original CCDF of the personal income data of Brazil.

physics.soc-ph↗

arXiv2016

Tsallis statistics in the income distribution of Brazil

This paper discusses the empirical evidence of Tsallis statistical functions in the personal income distribution of Brazil. Yearly samples from 1978 to 2014 were linearized by the q-logarithm and straight lines were fitted to the entire range of the income data in all samples, producing a two-parameters-only single function representation of the whole distribution in every year. The results showed that the time evolution of the parameters is periodic and plotting one in terms of the other reveals a cycle mostly clockwise. It was also found that the empirical data oscillate periodically around the fitted straight lines with the amplitude growing as the income values increase. Since the entire income data range can be fitted by a single function, this raises questions on previous results claiming that the income distribution is constituted by a well defined two-classes-base income structure, since such a division in two very distinct income classes might not be an intrinsic property of societies, but a consequence of an a priori fitting-choice procedure that may leave aside possibly important income dynamics at the intermediate levels.

econ.GN↗

arXiv2014

Galaxy Cosmological Mass Function

We study the galaxy cosmological mass function (GCMF) in a semi-empirical relativistic approach using observational data provided by galaxy redshift surveys. Starting from the theory of Ribeiro & Stoeger (2003, arXiv:astro-ph/0304094) between the mass-to-light ratio, the selection function obtained from the luminosity function (LF) data and the luminosity density, the average luminosity $L$ and the average galactic mass $\mathcal{M}_g$ are computed in terms of the redshift. $\mathcal{M}_g$ is also alternatively estimated by a method that uses the galaxy stellar mass function (GSMF). Comparison of these two forms of deriving the average galactic mass allows us to infer a possible bias introduced by the selection criteria of the survey. We used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift range $0.5 < z < 5.0$ and its LF Schechter parameters in the B-band, as well as this sample's stellar mass-to-light ratio and its GSMF data. Assuming ${\mathcal{M}_{g_0}} \approx 10^{11} \mathcal{M}_\odot$ as the local value of the average galactic mass, the LF approach results in $L_{B} \propto (1+z)^{(2.40 \pm 0.03)}$ and $\mathcal{M}_g \propto (1+z)^{(1.1\pm0.2)}$. However, using the GSMF results produces $\mathcal{M}_g \propto (1+z)^{(-0.58 \pm 0.22)}$. We chose the latter result as it is less biased. We then obtained the theoretical quantities of interest, such as the differential number counts, to calculate the GCMF, which can be fitted by a Schechter function. The derived GCMF follows theoretical predictions in which the less massive objects form first, being followed later by more massive ones. In the range $0.5 < z < 2.0$ the GCMF has a strong variation that can be interpreted as a higher rate of galaxy mergers or as a strong evolution in the star formation history of these galaxies.

astro-ph.GA↗