Joaquin Estevez-Delgado

We present the construction and analysis of a two-parameter family of exact solutions involving a regular, minimally coupled scalar field Φ with a self-interaction potential V(Φ) in a static and spherically symmetric spacetime. The solution contains two parameters: μ, which is related to the ADM mass, and λ, which determines the asymptotic structure. For λ = 0, the spacetime is asymptotically flat, whereas λ > 0 and λ < 0 yield anti-de Sitter and de Sitter behavior, respectively. In the latter two cases, the effective cosmological constant arises from the asymptotic behavior of the potential. A characteristic feature of the solution is that the scalar field is monotonic and bounded throughout the domain, including the limit R → 0, where the geometry is singular. The value μ = 1/3 separates a timelike singularity from a spacelike singularity and reduces the algebraic divergences of the curvature invariants to logarithmic divergences without regularizing the central endpoint. The asymptotic analysis, the analytic curve of double roots, and a numerical study of the number of zeros reveal a family with a Killing horizon associated with a black hole, a family with a cosmological horizon, and, in the de Sitter sector, configurations with two simple horizons that bound a static region.

We present a stellar model in the frame of Einstein’s general relativity considering a static and spherically symmetric spacetime which contains a perfect fluid. The analytical solution is determined starting from a temporal metric function that facilitates the integration of the system. We show that the state equation associated to the model can be approximated in the form [ ], where [ ] is the density on the surface of the star. The stability under adiabatic and radial perturbations of static, compact stellar objects with sources of matter from a perfect fluid will determine the maximum value of compactness [ ], the model also is stable according to the criteria of Harrison–Zeldovich–Novikov. In a complementary manner, the model is verified for the observational data of the compact object XMMU J173203.3-344518 in HESS J1731-347, of low mass [ ] and radius [ ][ ]km, from these we find that the maximum density occurs in the center for its maximum compactness.

We present a numerical model to simulate the atmospheric entry of meteoroids, focusing on the dynamic evolution of key parameters such as mass, velocity, pressure and energy deposition. Our model is based on a modified system of differential equations that builds upon the classic Opik formulation but allows greater flexibility by incorporating nonanalytic atmospheric density profiles and arbitrary meteoroid shapes. A distinguishing feature of this approach is the estimation of the flight angle directly from the velocity components, without requiring an explicit trajectory equation. To validate our model, we simulate the 2013 Chelyabinsk meteoroid event, obtaining break-up and burst altitudes of 55[ ]km and 33[ ]km, respectively, consistent with observational data. The model also reproduces pressure, energy deposition and debris cloud evolution, demonstrating its potential for accurate risk assessment and atmospheric entry predictions for near-Earth objects.

In this paper, we present and analyze a solution of the equations which describe a compact anisotropic star in the frame of Rastall’s theory of gravity. With the objective of performing a comparison and analyzing the impact of the Rastall parameter we will start from a known solution for Einstein’s theory of general relativity and we will generalize it into a model in the frame of Rastall’s gravity which will be dependent on two parameters, the Rastall [ ] and the anisotropy [ ], the interval of values for these is bounded when imposing the physical condition and the condition that the geometry is regular. Particular values of the parameters are employed in the analysis of the solution, considering the observational data of the neutron star PSR J0437–4715 which has a mass [ ] and radius [ ] km. The analysis shows that the density, pressure and speed of sound are altered by the value of the Rastall parameter, with a maximum central density [ ] kg/m³ for the maximum Rastall parameter considered. Also, it is shown that the solution is stable according to the adiabatic index criteria and the cracking condition.

In the frame of the nonconservative gravitational theory of Rastall, a solution is presented to the set of equations which originates from this theory in order to model the interior of a compact object in a static and spherically symmetric space–time with matter from a perfect charged fluid. In a particular manner, we realize an analysis of the solution considering the observational data of the star Her X-1, (mass [ ] [ ] and radius [ ] [ ]km), with a particular emphasis on the impact the Rastall parameter [ ] has on the behavior of the density, pressure and intensity of the electric field as well as on the stability conditions of the solution. It is shown that the condition which restricts the values of the maximum charge is the behavior of the pressure on the surface of the compact object. It is also shown that the central density [ ] [ ]kg/m³ for the lowest compactness, meanwhile [ ] [ ]kg/m³ for the highest compactness, obtaining, for this case, the maximum values of density when [ ]. In addition, an approximate equation of state is obtained in the form [ ], where [ ] denote the central pressure, the central density and the density on the surface of the star, respectively, while m and n are different exponents for each compactness value.

In this investigation report, we present the analysis of a stellar model formed by ordinary matter and quintessence-type matter in the frame of Rastall’s gravitation theory. The ordinary matter with a state equation for the radial pressure [ ], where [ ] is the so called MIT Bag constant and the quintessence-type matter, with density [ ] and tangential state equation of the form [ ], with [ ]. Through an analytic and graphic analysis, it is shown that the proposal is consistent with the expected behavior of the hydrostatic functions and, in particular, it’s focused on the analysis taking the observational data of the mass [ ] and radius [ ] [ ]km corresponding to the star PSR [ ]. We obtain the central density of the ordinary matter [ ] [ ]kg/m³ and the MIT Bag constant [ ] which changes depending on the compactness and the Rastall parameter but its values are independent from the parameter of the quintessence matter w.

In this paper, we study the synchronization of three Piecewise Linear (PWL) Rössler systems that exhibit coexistence of two attractors, coupled in linear configuration. In particular, we analyze the four linear configurations of the network motifs. We analyze the interaction of the systems by varying the unidirectional or bidirectional coupling strengths depending on the case under study, in order to characterize the conditions under which complete synchronization between the three PWL Rössler systems are obtained. We have found, by means of the error functions, the range of values of the coupling strengths where the different types of synchronization occurs. The numerical results show that the interaction of various multistable chaotic systems causes different types of synchronization and very complex dynamics between the systems.

A new interior solution of Einstein’s equations is derived for a static and spherically symmetric space–time that contains fluid with anisotropic pressures, characterized by a parameter N. The model presented is a generalization to a proposal which contemplated a perfect fluid, which allows us to do an analysis of the impact of the anisotropy on the compactness, density and speed of sound. Taking the observational data of the mass [ ] and radius [ ] km as well as the mass [ ] and radius [ ]km reported for the star EXO 1745-248, it is determined that the range of values of the density varies between [ ] and [ ] and these increase as the anisotropy parameter increases; it also shows an effect of the anisotropy on the speed of sound. The stability of the solution is shown through the Zeldovich criteria and through the adiabatic index, and from a graphic analysis it is verified that the behavior of the density, pressures and speed of sound are physically acceptable.