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Motivated by the impact of the phantom field (or anti-Maxwell field) on the structure of three-dimensional black holes in the presence of the cosmological constant, we present the first extraction of solutions for the phantom BTZ (A)dS black hole. In this study, we analyze the effect of the phantom field on the horizon structure. Furthermore, we compare the BTZ black holes in the presence of both the phantom and Maxwell fields. Additionally, we calculate the conserved and thermodynamic quantities of the phantom BTZ black holes, demonstrating their compliance with the first law of thermodynamics. Subsequently, we assess the effects of the electrical charge and the cosmological constant on the local stability in the canonical ensemble by considering these fields with respect to the heat capacity. We then investigate the global stability area of the BTZ black holes with phantom and Maxwell fields within the grand canonical ensemble using Gibbs free energy. In this analysis, we evaluate the influence of the electrical charge and the cosmological constant on this area., Comment: 12 pages

In the framework of Simpson-Visser, the search for field sources that produce black bounces in alternative gravity theories has remained unresolved. In this paper, the first in a series exploring sources for alternative theories of gravity, we identify such a source for the $2+1$ dimensional K-gravity black bounce. The K-gravity black hole is notable for allowing asymptotically locally flat solutions in lower-dimensional spacetime, yet it possesses curvature singularities concealed within the event horizon. Using the Simpson-Visser regularization technique, we eliminate this singularity, constructing asymptotically locally flat black-bounce solutions in $2+1$ dimensions. We explore the causal structure of these solutions, identifying the conditions under which they describe regular black holes or wormholes. By calculating curvature invariants, we confirm the absence of singularities within the event horizon. Additionally, we demonstrate that, beyond non-linear electrodynamics, a non-linear scalar field is required to source the solution. Finally, we investigate the geodesic structure of this spacetime, analyzing the trajectories of both massive and massless particles. We also confirm the existence of circular orbits and assess their stability., Comment: 28 pages, 12 figures

In the present work, we obtain and analyze a new class of analytical solutions of magnetically charged black bounces in k-essence theory, spherically symmetric in (3+1)-dimensions, coupled to nonlinear electrodynamics (NED). We consider two metric models, Simpson-Visser and Bardeen, for the k-essence configurations n = 1/3 and n = 1/5. We obtain in an analytical way which scalar field, field potential, and Lagrangian NED are necessary to support the metrics. We analyze the behavior of these quantities and the energy conditions due to the scalar field and the NED.

The relationships between workload and fatigue or sleepiness are investigated through the analysis of rosters and responses to questionnaires from Brazilian aircrews, taken from Fadig\^ometro database. The approach includes temporal markers - coinciding with Samn-Perelli (SP) and Karolinska Sleepiness Scale (KSS) responses - where SAFTE-FAST model outcomes are calculated. The model results follow the increase of fatigue and sleepiness perceptions during the dawn (0h00 to 05h59), but underestimate the self-rated scores during the evening (18h00 to 23h59). On the other hand, the KSS scores fit the relative risk of pilot errors, representing a reasonable proxy for risk assessment. Linear relationships obtained between workload metrics, computed within 168-hours prior to the responses, and self-rated SP and KSS scores provide a consistent method to estimate accumulated fatigue and sleepiness. Considering 7149 rosters of 2023, the duty time ($DT$), the number of flight sectors ($N_{CREW}$) and the sum of flight sectors with sit periods longer than one hour ($N_{CREW}+N_{SIT}$) are associated with 70.1%/60.6% of the highest predicted scores of SP/KSS. Applying the mitigations $DT\leq44h$, $N_{CREW}\leq15$ and $N_{CREW}+N_{SIT}\leq19$ for every 168-hour interval yields a significant decrease in the higher values of SP/KSS with minimal impact on aircrew productivity., Comment: 16 pages and 5 figures

We consider a recently introduced extension of General Relativity dubbed as Cotton gravity (CG), based on the use of the Cotton tensor, to estimate the size of a new constant $\gamma$ appearing within a spherically symmetric, vacuum solution of the theory. Taking into account its non-asymptotically flat character, we use the inferred size of the central brightness depression of the supermassive object at the heart of the Milky Way galaxy (Sgr A*) by the Event Horizon Telescope to constrain at $2\sigma$ the CG parameter as $\gamma M \approx 3.5 \times 10^{-12}$. We study the potential observational consequences from the smallness of such a value using exact and numerical expressions for the deflection angle, optical images from optically and geometrically thin accretion disks, isoradials, and instability scales (Lyapunov index) of nearly bound geodesics associated to photon rings. Our results point towards the impossibility to distinguish between these two geometries using current and foreseeable techniques in the field of interferometric detection of optical sources., Comment: 13 pages, 8 figures

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as ''Cotton gravity'' (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson-Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG., Comment: 14 pages, 6 figures

This study delves deeply into braneworld scenarios within modified gravity models, investigating their impact on particle localization and the structure of branes. Through a comprehensive blend of numerical analyses and theoretical inquiries, we unravel a nuanced correlation between deviations from standard General Relativity (GR) and the emergence of split branes. By employing probabilistic measurements, we pinpoint stable configurations that align with brane division intervals, thus challenging prevailing assumptions regarding the gravitational framework of our universe. Furthermore, our investigation extends to the localization of fermions within the brane, exposing intricate dynamics shaped by scalar field characteristics and modifications to gravitational models. By harnessing quantum information measurements, notably Shannon entropy, we discern heightened probabilities of fermion localization within the brane as gravitational models diverge from standard paradigms. This underscores the limitations of General Relativity in comprehensively describing the complexities inherent in our universe. Lastly, our exploration of massive fermions unveils their potential to breach the confines of the brane, hinting at promising avenues for future experimental endeavors aimed at probing the nature of extra dimensions and gravitational interactions. This suggests exciting prospects for advancing our understanding of fundamental physics beyond conventional boundaries.

In this work, we analyse black bounce solutions in the recently proposed ``Conformal Killing gravity'' (CKG), by coupling the theory to nonlinear electrodynamics (NLED) and scalar fields. The original motivation of the theory was essentially to fulfil specific criteria that are absent in existing gravitational theories, namely, to obtain the cosmological constant as an integration constant, derive the energy-momentum conservation law as a consequence of the gravitational field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. In this work, we extend the static and spherically symmetric solutions obtained in the literature, and explore the possibility of black bounces in CKG, coupled to NLED and scalar fields. We find novel NLED Lagrangian densities and scalar potentials, and extend the class of black bounce solutions found in the literature. Furthermore, within black bounce geometries, we find generalizations of the Bardeen-type and Simpson-Visser geometries and explore the regularity conditions of the solutions., Comment: 13 pages, 12 figures. Accepted for publication in EPJC

In the present study, we generalize the possible ghost field configurations within the framework of $k$-essence theory to the Simpson-Visser metric area function $\Sigma^2=x^2+a^2$. Our analysis encompasses field configurations for the region-defined metric function $dA_\pm$ as well as the general solution that asymptotically behaves as Schwarzschild-de Sitter for $x\to-\infty$. Specifically, we investigate two scalar field configurations and define the associated potential for each one. Through rigorous calculations, we verify that all equations of motion are satisfied. Notably, our findings indicate that even when proposing new configurations of ghost scalar fields, the energy conditions remain unchanged. This result serves to validate the wormhole solutions obtained in previous studies., Comment: 25 pages, 7 figures

In this work, we study timelike and lightlike geodesics in Kalb-Ramond (KR) gravity around a black hole with the goal of constraining the Lorentz symmetry-breaking parameter $l$. The analysis involves studying the precession of the S2 star periastron orbiting Sgr A* and geodesic precession around the Earth. The ratio of precession frequencies for General Relativity (GR) and KR gravity is computed, with Event Horizon Telescope (EHT) results providing a parameter range for the spontaneous symmetry-breaking of $-0.185022 \leq l \leq 0.060938$. Utilizing the geodesic precession frequency from the Gravity Probe B (GP-B), the $l$ parameter is further constrained to $-6.30714 \times 10^{-12} \leq l \leq 3.90708 \times 10^{-12}$, which is consistent with the Schwarzschild limits. Moreover, for timelike geodesics, the innermost circular orbit (ICO) and innermost stable circular orbit (ISCO) are determined and analyzed to illustrate the impact of the symmetry breaking term. Zoom-whirl obstructions are compared with the Schwarzschild solution. Lower and upper limits of the photon sphere for lightlike geodesics are established to demonstrate the influence of KR gravity on the photon sphere. Additionally, the shadow radius is determined for two observers, one situated at a finite distance from the KR black hole, and the other located at an infinite distance, to constrain the symmetry-breaking parameter $l$, with comparisons made to EHT results. The bounds for $l$ derived from constraints on the photon sphere radius for lightlike geodesics yield $-0.0700225 \leq l \leq 0.189785$ using EHT data. The findings of this paper align with experimental results in the $l \rightarrow 0$ limit., Comment: 11 pages, 4 figures

In this paper, we investigate the gravitational lensing effect for the Schwarzschild-like black hole spacetime in the background of a Kalb-Ramond (KR) field proposed in [K. Yang et. al., Phys. Rev. D 108 (2023) 124004]. The solution is characterized by a single extra parameter $l$, which is associated to the Lorentz symmetry breaking induced by the KR field. First, we calculate the exact deflection angle of massive and massless particles for finite distances using elliptic integrals. Then we study this effect in the weak and strong field regimes, discussing the correction of the KR parameter on the coefficients of the expansions in both limits. We also find that increasing $l$ decreases the deflection angle. Furthermore, we use the available data from the Sagittarius $A^{\star}$ object, which is believed to be a supermassive black hole at the center of our galaxy, to calculate relevant observables, such as, the image position, luminosity, and delay time. The values found could be potentially measured in the weak field regime, though for strong fields one would have to wait for the next generation of interferometers., Comment: 16 pages, 8 figures. V2: references added. arXiv admin note: text overlap with arXiv:2309.02658

In this work, the trajectories of particles around a black bounce spacetime are considered, with the Simpson-Visser model serving as an example. Trajectories for massless and massive particles are obtained through the study of null and time-like geodesics. As the Simpson-Visser solution is derived via the Einstein equations for a source involving nonlinear electrodynamics and a scalar field, photon trajectories are investigated by considering an effective metric in which photons follow null geodesics. The stability of circular orbits is analyzed by examining the behavior of maxima and minima of the effective potential associated with geodesics. It is also studied what type of geodesic photons follow when the usual metric is considered instead of the effective one. The main focus of this work is to obtain corrections to the trajectories of photons when considering that the solution arises from nonlinear electrodynamics., Comment: 17 pages, 10 figures. Published in International Journal of Theoretical Physics. V2: corrected typos, added references

One of the main issues in gravitation is the presence of singularities in the most common space-time solutions of General Relativity, as the case of black holes. A way of constructing regular solutions that remove spacelike singularities consists in implement a bounce on such space-time, leading to what is usually known as black bounce space-times. Such space-times are known to describe regular black holes or traversable wormholes. However, one of the main issues lies on reconstructing the appropriate source that leads to such a solution. In this paper, a reconstruction method is implemented to show that such types of metrics can be well accommodated in non-linear electrodynamics with the presence of a scalar field. Some of the most important black bounces solutions are reconstructed in this framework, both in 3+1 as in 2+1 dimensions. For the first time in the literature, these solutions have an electrically charged source of matter from non-linear electrodynamics. Specific features are indicated that distinguish electric sources from magnetic ones, previously found for the same space-times., Comment: V3: 14 pages, new figures, published in EPJC

In Atazadeh and Hadi (JCAP \textbf{01}, 067 (2024)), the authors proposed that black bounce solutions, such as the Simpson-Visser and the Bardeen-type spacetimes, can be obtained from Rastall gravity. To achieve these spacetimes, the authors consider the presence of a phantom scalar field with nonlinear electrodynamics. However, in this comment, we obtained different electromagnetic Lagrangians from the original work. The most problematic issue is not the incorrect expression of the electromagnetic Lagrangian itself. We show that the method obtains electromagnetic functions that are inconsistent. To obtain the black bounce spacetimes as solutions of Rastall gravity, it is necessary to consider an isotropic fluid, combined with the nonlinear electrodynamics and the phantom scalar field., Comment: Comment on arXiv:2311.07637. V2: Some typos corrected. Version published in JCAP

Motivated by high interest in Lorentz invariant massive gravity models known as dRGT massive gravity, we present an exact phantom black hole solution in this theory of gravity and discuss the thermodynamic structure of the black hole in the canonical ensemble. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics and the Smarr relation in the extended phase space. In addition, we investigate both the local and global stability of these black holes and show how massive parameters affect the regions of stability. We extend our study to investigate the optical features of the black holes such as the shadow geometrical shape, energy emission rate, and deflection angle. Also, we discuss how these optical quantities are affected by massive coefficients. Finally, we consider a massive scalar perturbation minimally coupled to the background geometry of the black hole and examine the quasinormal modes (QNMs) by employing the WKB approximation., Comment: 26 pages, 12 figures, 1 table

In this work, we consider an extension of the symmetric teleparallel equivalent of General Relativity (STEGR), namely, $f(\mathbb{Q})$ gravity, by including a boundary term $\mathbb{B}_Q$, where $\mathbb{Q}$ is the non-metricity scalar. More specifically, we explore static and spherically symmetric black hole and regular black hole solutions in $f(\mathbb{Q},\mathbb{B}_Q)$ gravity coupled to nonlinear electrodynamics (NLED). In particular, to obtain black hole solutions, and in order to ensure that our solutions preserve Lorentz symmetry, we assume the following relation $f_Q = -f_B$, where $f_{Q}=\partial f/\partial\mathbb{Q}$ and $f_{B}= \partial f/\partial\mathbb{B}_Q$. We develop three models of black holes, and as the starting point for each case we consider the non-metricity scalar or the boundary term in such a way to obtain the metric functions $A(r)$. Additionally, we are able to express matter through analytical solutions for specific NLED Lagrangians ${\cal L}_{\rm NLED}(F)$. Furthermore, we also obtain generalized solutions of the Bardeen and Culetu types of regular black holes, by imposing specific metric functions., Comment: 21 pages, 10 figures. V2: 25 pages, 15 figures; discussion and references added. Accepted for publication in EPJC

The geodesic method has played a crucial role in understanding the circular orbits generated by compact objects, culminating in the definition of the photon sphere, which was later generalized to a photon surface in arbitrary spacetimes. This new formulation extends the concept of the photon sphere in a broader sense, including dynamical spacetimes, as shown by the Vaidya solution. The photon surface essentially defines the null geodesics, which are originally tangent to the temporal surface, and keeps them confined to this surface. However, this formalism does not cover all classes of particles, and to overcome this limitation, a more comprehensive approach, denoted as the "massive particle surface", has been proposed that also accounts for charged massive particles. Indeed, the photon surface concept is recovered when the charge and mass of the particles are zero. In this work, we use these three formalisms to check the consistency of the results for the values of the radius of the photon sphere ($r_{ps}$) and the radius of the "innermost stable circular orbit" (ISCO) ($r_{\rm ISCO}$) for some gravitational models. In our results, the first model is described by conformal gravity, with the peculiarity that $g_{00}\neq-g_{11}^{-1}$. The second model, i.e. the Culetu solution, is developed by coupling General Relativity with nonlinear electrodynamics, which requires the consideration of the effective metric ($g_{\rm eff}^{\mu\nu}$) for geodesic approaches. Furthermore, we have also analysed the expressions for $r_{ps}$ and $r_{\rm ISCO}$ in a general static and spherically symmetric metric. Under these circumstances, we have found a discrepancy of $r_{ps}$ and $r_{\rm ISCO}$ obtained by the massive particle surface formalism as compared to the geodesic and photon surface formalisms., Comment: 15 pages, 1 figure; comments are welcome

In this paper we try to clarify that a regular metric can generate a singular spacetime. Our work focuses on a static and spherically symmetric spacetime in which regularity exists when all components of the Riemann tensor are finite. There is work in the literature that assumes that the regularity of the metric is a sufficient condition to guarantee it. We study three regular metrics and show that they have singular spacetime. We also show that these metrics can be interpreted as solutions for black holes whose matter source is described by nonlinear electrodynamics. We analyze the geodesic equations and the Kretschmann scalar to verify the existence of the curvature singularity. Moreover, we use a change of the line element $r \rightarrow \sqrt{r^2+a^2}$, which is a process of regularization of spacetime already known in the literature. We then recompute the geodesic equations and the Kretschmann scalar and show that all metrics now have regular spacetime. This process transforms them into black-bounce solutions, two of which are new. We have discussed the properties of the event horizon and the energy conditions for all models., Comment: 26 pages, 9 figures

In this work, we explore black hole and regular black hole solutions in the recently proposed Conformal Killing Gravity (CKG). This theory is of third order in the derivatives of the metric tensor and essentially satisfies three theoretical criteria for gravitational theories beyond General Relativity (GR). The criteria essentially stipulate the following, that one should: (i) obtain the cosmological constant as an integration constant; (ii) derive the energy conservation law as a consequence of the field equations, rather than assuming it; (iii) and not necessarily consider conformally flat metrics as vacuum solutions. In fact, existing modified theories of gravity, including GR, do not simultaneously fulfil all of these three criteria. Here, we couple CKG to nonlinear electrodynamics (NLED) and scalar fields, and we explore solutions of black holes and regular black holes. More specifically, by solving the field equations of CKG, we find specific forms for the NLED Lagrangian, the scalar field and the field potential, and analyse the regularity of the solutions through the Kretschmann scalar. We find generalizations of the Schwarschild--Reissner-Nordstr\"{o}m--AdS solutions, and consequently further extend the class of (regular) black hole solutions found in the literature., Comment: 13 pages, 10 figures. V2: matches published version

In this article, the implementation of black-bounce solutions in $f(R)$ theories is investigated. Black-bounce solutions are regular configurations of the static spherically symmetric space-time, containing both black holes and wormholes structures. In General Relativity (GR), black-bounce solution implies violation of the energy conditions. We investigate the same issue in $f(R)$ theories using two strategies: first, supposing a given form for the $f(R)$ function and then determining the matter behavior; second, imposing a condition on the matter density and obtaining the resulting $f(R)$ function. In all cases, a given structure for the metric functions is supposed. Violation of the energy conditions still occur but they are less severe than in the corresponding GR cases. We propose a zero-density model that has horizons, which differs from the GR case. We also propose a model with positive energy density and show that $\rho+p_r>0$, which was not the case in GR., Comment: 9 pages, 4 figures

In the present work, we construct black-bounce configurations in the context of $k$-essence theory. The solutions have a regular metric function at the origin. The area metric function is linked to the black-bounce area initially considered by Simpson-Visser, $\Sigma^2=x^2+a^2$. Subsequently, the expressions for the scalar field and scalar potential corresponding to the found solutions are determined, exhibiting phantom behavior everywhere due to violation of Null Energy Condition $(NEC^\phi)$. The Kretschmann scalar is regular throughout spacetime, and the geodesics are complete. The energy conditions are analyzed, verifying that the null $(NEC^\phi_1)$ and dominant energy conditions $(DEC^\phi_1)$ are violated inside and outside the event horizon. Finally, the extrinsic curvature method was applied to determine the sign of the mass on the junction surface., Comment: 13 pages, 15 figures

In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main necessary theorems. We discuss the implementation of useful algebraic topology tools to characterize representations., Comment: 14 pages, to appear as a chapter in "Tribute to Ruben Aldrovandi", ed. by F. Caruso, J. G. Pereira, A. Santoro (Editora Livraria da F\'isica, S\~ao Paulo, 2024)

In this paper we study the gravitational lensing effect for the Schwarzschild solution with holonomy corrections. We use two types of approximation methods to calculate the deflection angle, namely the weak and strong field limits. For the first method, we calculate the deflection angle up to the fifth order of approximation and show the influence of the parameter $\lambda$ (in terms of loop quantum gravity) on it. In addition, we construct expressions for the magnification, the position of the lensed images and the time delay as functions of the coefficients from the deflection angle expansion. We find that $\lambda$ increases the deflection angle. In the strong field limit, we use a logarithmic approximation to compute the deflection angle. We then write four observables, in terms of the coefficients $b_1$, $b_2$ and $u_m$, namely: the asymptotic position approached by a set of images $\theta_{\infty}$, the distance between the first image and the others $s$, the ratio between the flux of the first image and the flux of all other images $r_m$, and the time delay between two photons $\Delta T_{2,1}$. We then use the experimental data of the black hole Sagittarius $A^{\star}$ and calculate the observables and the coefficients of the logarithmic expansion. We find that the parameter $\lambda$ increases the deflection angle, the separation between the lensed images and the delay time between them. In contrast, it decreases the brightness of the first image compared to the others., Comment: 26 pages, 17 figures

In this paper, we will use the coincident gauge to investigate new solutions of the f(Q) theory applied in the context of black holes, regular black holes, and the black-bounce spacetime. For each of these approaches, we compute the linear solutions and the solutions with the constraint that the non-metricity scalar is zero. We also analyze the geodesics of each solution to interpret whether the spacetime is extensible or not, find the Kretschmann scalar to determine the regularity along spacetime, and in the context of regular black holes and black-bounce, we calculate the energy conditions. In the latter black-bounce case we realize that the null energy condition $(NEC)$, specifically the $NEC_1=WEC_1=SEC_1\leftrightarrow \rho+p_{r}\geq 0$, is satisfied outside the event horizon., Comment: 30 pages, 1 figure

We apply the Simpson-Visser phenomenological regularization method to a cylindrically symmetric solution of the Einstein-Maxwell equations known as an inverted black hole. In addition to analyzing some properties of thus regularized space-time, including the Carter-Penrose diagrams, we show that this solution can be obtained from the Einstein equations with a source combining a phantom scalar field with a nonzero self-interaction potential and a nonlinear magnetic field. A similar kind of source is obtained for the cylindrical black bounce solution proposed by Lima et al. as a regularized version of Lemos's black string solution. Such sources are shown to be possible for a certain class of cylindrically, planarly and toroidally symmetric metrics that includes the regularized solutions under consideration., Comment: 14 pages, 9 figures. V2: Fixed misprints, some references added. Published in the PRD

In this paper we propose to use Shapiro time delay as a tool to distinguish between different black hole solutions. We calculate the analytic Shapiro time, using first-order expansions, for four solutions. They are Schwarzschild, Reissner-Nordstr\"o{}m, Bardeen, and Ay\'on-Beato and Garc\'ia. We created a numerical experiment, based on measurements made in the solar system, consisting of the round trip path of light passing through a black hole at the center. We obtained different delay times varying between the order of $10^{-4}$s and $10^{-6}$s, for a stellar black hole; and variations of the order of hours, for a supermassive one. Considering that the accuracy currently achieved in measurements made in the solar system are on the order of $10^{-12}$s, we believe that this mechanism could be used in black hole model determination in the near future.

In this paper, we obtain exact phantom (A)dS black hole solutions in the context of $F(R)$ gravity with topological spacetime in four dimensions. Then, we study the effects of different parameters on the event horizon. In the following, we calculate the conserved and thermodynamic quantities of the system and check the first law of thermodynamics for these kinds of black holes. Next, we evaluate the local stability of the topological phantom (A)dS black holes in $F(R)$ gravity by studying the heat capacity and the geometrothemodynamic, where we show that the two approaches agrees. We extend our study and investigate global stability by employing the Gibbs potential and the Helmholtz free energy. In addition, the effects of different parameters on local and global stabilities will be highlighted., Comment: 10 pages, 5 figures, 1 table

Black bounces are spacetimes that can describe, depending on certain parameters, black holes or wormholes. In this work, we use a method to obtain the matter content that generates black bounce solutions in general relativity. The method is constructed in a general way, and as models, we apply it to the Simpson--Visser black bounce solution and the Bardeen-type black bounce solution. We obtain that these metrics are solutions of Einstein's equations when we consider the coupling of the gravitational interaction with a phantom scalar field with a nonlinear electrodynamics. The presence of the phantom scalar field is linked to the fact that this type of solution violates the null energy condition. We analyze separately the energy conditions associated with the stress-energy tensor for the scalar field and for the electromagnetic field., Comment: 13 pages, 5 figures, Accepted for publication in Phys. Rev. D

In this paper we present a Bardeen solution surrounded by a cloud of strings fluid. We show how this model has the same event horizon characteristic as the Bardeen solution, however, the parameter of the strings make the solution singular at the origin. We also analyze the solution from a thermodynamic point of view. We calculate the system's state function, enthalpy; the temperature; and the other potentials; as a function of entropy. By analyzing the thermodynamic coefficients, we show that the solution presents three distinct phases, two of which are stable and one unstable. These three phases could be best visualized using a plot of Gibbs free energy versus temperature. In the end, we calculate the critical exponents and find that they are the same as those found in Van der Walls theory., Comment: 16 pages, 12 figures

A string is the one-dimensional generalization of a point particle. In this sense, the analog of a cloud of dust would be a cloud of strings. In this work, we consider a cloud of strings around a regular solution in general gelativity. We consider the Bardeen solution and the Simpson--Visser solution, analyzing the consequences of the cloud in the regularity and in the energy conditions. Actually, the presence of the cloud could make the energy density positive when compared to the Simpson--Visser case. We verify that the usual Bardeen solution becomes singular in the presence of the cloud of string while the Simpson--Visser solution is still regular, violating the energy conditions, as the usual solution. We also calculate some thermodynamic quantities to evaluate how a cloud of strings influences the thermodynamics of the solutions., Comment: 14 pages, 2 figures, accepted for publication in PRD

Simulated Moving Bed (SMB) chromatography is a well-known technique for the resolution of several high-value-added compounds. Parameters identification and model topology definition are arduous when one is dealing with complex systems such as a Simulated Moving Bed unit. Moreover, the large number of experiments necessary might be an expansive-long process. Hence, this work proposes a novel methodology for parameter estimation, screening the most suitable topology of the models sink-source (defined by the adsorption isotherm equation) and defining the minimum number of experiments necessary to identify the model. Therefore, a nested loop optimization problem is proposed with three levels considering the three main goals of the work: parameters estimation; topology screening by isotherm definition; minimum number of experiments necessary to yield a precise model. The proposed methodology emulated a real scenario by introducing noise in the data and using a Software-in-the-Loop (SIL) approach. Data reconciliation and uncertainty evaluation add robustness to the parameter estimation adding precision and reliability to the model. The methodology is validated considering experimental data from literature apart from the samples applied for parameter estimation, following a cross-validation. The results corroborate that it is possible to carry out trustworthy parameter estimation directly from an SMB unit with minimal system knowledge.

The flavor is the focal point in the flavor industry, which follows social tendencies and behaviors. The research and development of new flavoring agents and molecules are essential in this field. On the other hand, the development of natural flavors plays a critical role in modern society. In light of this, the present work proposes a novel framework based on Scientific Machine Learning to undertake an emerging problem in flavor engineering and industry. Therefore, this work brings an innovative methodology to design new natural flavor molecules. The molecules are evaluated regarding the synthetic accessibility, the number of atoms, and the likeness to a natural or pseudo-natural product., Comment: 24 pages, 8 figures

Scientific machine learning (SciML) is a field of increasing interest in several different application fields. In an optimization context, SciML-based tools have enabled the development of more efficient optimization methods. However, implementing SciML tools for optimization must be rigorously evaluated and performed with caution. This work proposes the deductions of a robustness test that guarantees the robustness of multiobjective SciML-based optimization by showing that its results respect the universal approximator theorem. The test is applied in the framework of a novel methodology which is evaluated in a series of benchmarks illustrating its consistency. Moreover, the proposed methodology results are compared with feasible regions of rigorous optimization, which requires a significantly higher computational effort. Hence, this work provides a robustness test for guaranteed robustness in applying SciML tools in multiobjective optimization with lower computational effort than the existent alternative.

In this article, we test the possibility of building new black-bounce spacetimes with changes in the area in the context of general relativity in four dimensions. These new metrics can present extra structures, such as anti-throats. We see two regions where the area goes to infinity, and, depending on the model, one of these regions presents curvature singularities. Regular metrics can be extended to negative values of the radial coordinate and have a symmetrical structure, whereas some singular cases cannot be extended and have no symmetrical structure. The energy conditions are analyzed, and, for some cases, at least one of the inequalities in the null energy condition is not respected. We also presented models that satisfied the null energy condition outside the event horizon. The event horizon hides the throats of these models., Comment: Revised text, addition of Penrose diagrams, removal of figures and equations

In this work we analyze a solution that mimics the Bardeen solution with a cosmological constant surrounded by quintessence. We show that this solution can be obtained by Einstein equations coupled with nonlinear electrodynamics. We also show that the solution is not always regular and what the conditions for regularity are. We analyze the thermodynamics associated with this type of solution by establishing the form of the Smarr formula and the first law of thermodynamics. We obtain some thermodynamic quantities such as pressure, temperature, heat capacity and isothermal compressibility. Once we have these thermodynamic quantities, we check if this solution has phase transitions and how it behaves at the points where the transitions occur. For some values of the parameters, we find that the solution exhibits a first-order phase transition, like a van der Waals fluid., Comment: 17 pages, 9 figures. Published version

We study new solutions of black bounce spacetimes formulated in $f(T)$ gravity in four dimensions. First, we present the case of a diagonal tetrad, where a constraint arises in the equations of motion, which is divided into the cases of null torsion, constant torsion, and Teleparallel. The Null Energy Condition (NEC) is still always violated, which implies that the other energy conditions are violated. The solutions are regular in all spacetime and the solution with null torsion exhibits discontinuity between the energy conditions outside and inside the event horizon. Second, we present the case of non-diagonal tetrads. This case is divided into a Simpson-Visser type model and a quadratic model. The NEC continues to be violated, implying a violation of the other energy conditions. The solutions are regular in all spacetimes. An interesting result is that due to the possibility that the area associated with the metric is different from $4\pi r^2$, the no-go theorem established in the usual $f(T)$ is violated, appearing the new possibility $g_{00}=-g^{11}$, for the components of the metric., Comment: 24 pages, 9 figures

This work evaluates the potential root causes of fatigue using a biomathematical model and a robust sample of aircrew rosters from the Brazilian regular aviation. The fatigue outcomes derive from the software Sleep, Activity, Fatigue, and Task Effectiveness Fatigue Avoidance Scheduling Tool (SAFTE-FAST). The average minimum SAFTE-FAST effectiveness during critical phases of flight decreases cubically with the number of shifts that elapse totally or partially between mid-night and 6 a.m. within a 30-day period ($N_{NS}$). As a consequence, the relative fatigue risk increases by 23.3% (95% CI, 20.4-26.2%) when increasing $N_{NS}$ from 1 to 13. The average maximum equivalent wakefulness in critical phases also increases cubically with the number of night shifts and exceeds 24 hours for rosters with $N_{NS}$ above 10. The average fatigue hazard area in critical phases of flight varies quadratically with the number of departures and landings within 2 and 6 a.m. ($N_{Wocl}$). These findings demonstrate that both $N_{NS}$ and $ N_{Wocl}$ should be considered as key performance indicators and be kept as low as reasonably practical when building aircrew rosters. The effectiveness scores at 30 minute time intervals allowed a model estimate for the relative fatigue risk as a function of the time of the day, whose averaged values show reasonable qualitative agreement with previous measurements of pilot errors. Tailored analyses of the SAFTE-FAST inputs for afternoon naps before night shifts, commuting from home to station and vice-versa, and bedtime before early-start shifts show relevant group effects ($p < 0.001$) comparing the groups with and without afternoon naps, with one or two hours of commuting and with or without the advanced bedtime feature of the SAFTE-FAST software, evidencing the need of a better and more accurate understanding of these parameters when modelling fatigue risk factors., Comment: 17 pages and 6 figures

Paper holds the promise to replace silicon substrates in applications like internet of things or disposable electronics that require ultra-low-cost electronic components and an environmentally friendly electronic waste management. In the last years, spurred by the abovementioned properties of paper as a substrate and the exceptional electronic, mechanical and optical properties of van der Waals (vdW) materials, many research groups have worked towards the integration of vdW materials-based devices on paper. Recently, a method to deposit a continuous film of densely packed interconnects of vdW materials on paper by simply rubbing the vdW crystals against the rough surface of paper has been presented. This method utilizes the weak interlayer vdW interactions and allows cleaving of the crystals into micro platelets through the abrasion against the paper. Here, we aim to illustrate the general character and the potential of this technique by fabricating films of 39 different vdW materials (including superconductors, semi-metals, semiconductors, and insulators) on standard copier paper. We have thoroughly characterized their optical properties showing their high optical quality: one can easily resolve the absorption band edge of semiconducting vdW materials and even the excitonic features present in some vdW materials with high exciton binding energy. We also measured the electrical resistivity for several vdW materials films on paper finding exceptionally low values, which are in some cases, orders of magnitude lower than those reported for analogous films produced by inkjet printing. We finally demonstrate the fabrication of field-effect devices with vdW materials on paper using the paper substrate as an ionic gate., Comment: 4 figures in main text, 21 figures in Supp. Info

We discuss the great importance of using mathematical software in solving problems in today's society. In particular, we show how to use Mathematica software to solve ordinary differential equations exactly and numerically. We also show how to represent these solutions graphically. We treat the particular case of a charged particle subject to an oscillating electric field in the xy plane and a constant magnetic field. We show how to construct the equations of motion, defined by the vectors position, velocity, electric and magnetic fields. We show how to solve these equations of Lorentz force, and graphically represent the possible trajectories. We end by showing how to build a video simulation for an oscillating electric field trajectory particle case., Comment: 14 pages, 14 figures

In this work, new solutions for regular black holes that have multihorizons are proposed. These are formed by the direct product of solutions already published in the literature, which are described through the coupling of gravity with nonlinear electrodynamics. We analyze the regularity of the spacetime, the electric field, and the energy conditions of each solution. The strong energy condition is always violated within the event horizon in all solutions, while other energy conditions depend on the ratio between extreme charges of isolated solutions. For solutions with four horizons, we present two examples, Bardeen-Culetu and Balart-Culetu. Both solutions are regular, but the first do not satisfy all the energy conditions, except the strong, because it has an extreme charge ratio of 1.57581, great value. The second solution, on the other hand, can satisfy all other energy conditions, except the SEC, and has an extreme charge ratio of 1.09915, a value that allows this feature. It's also proposed a regular solution with up to six horizons, Balart-Culetu-Dymnikova, where, for a given charge value, we can verify that it satisfies all energy conditions, except the strong one. This was possible due to the ratio between extreme charges that are neither too high nor too close. We propose solutions with any number of horizons. We show that points where $-F(r)$ has a non null minimum represent a cusp in the Lagrangian $-L(F)$. We also show an example of multihorizon solution with magnetic charge. Multihorizon solutions may exhibit exotic properties, such as negative energy density, or violation of energy conditions, but which can be circumvented with a selected choice of customized solutions and extreme charge values, resulting in regular black hole solutions that satisfy all energy conditions, less the strong., Comment: 17 pages, 18 figures

We develop a number of novel "black-bounce" spacetimes. These are specific regular black holes where the "area radius" always remains non-zero, thereby leading to a "throat" that is either timelike (corresponding to a traversable wormhole), spacelike (corresponding to a "bounce" into a future universe), or null (corresponding to a "one-way wormhole"). We shall first perform a general analysis of the regularity conditions for such a spacetime, and then consider a number of specific examples. The examples are constructed using a mass function similar to that of Fan--Wang, and fall into several particular cases, such as the original Simpson--Visser model, a Bardeen-type model, and other generalizations thereof. We shall analyse the regularity, the energy conditions, and the causal structure of these models. The main results are several new geometries, more complex than before, with two or more horizons, with the possibility of an extremal case. We shall derive a general theorem regarding static space-time regularity, and another general theorem regarding (non)-satisfaction of the classical energy conditions., Comment: V1: 26 pages, 13 figures. V2: Still 26 pages, 13 figures; 7 references added, plus some historical comments. No physics changes. V3: Now 27 pages, still 13 figures. Title change, new section on volume quantifier integral on pg 8, new calculation Eq.~(56) on pg 10, additional discussion pg 11, 2 new references added, bibliography tidied

In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,\epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated., Comment: 12 pages, 8 figures

In this work, we study the existence of regular black holes solutions with multihorizons in general relativity and in some alternative theories of gravity. We consider the coupling between the gravitational theory and nonlinear electrodynamics. The coupling generates modifications in the electromagnetic sector. This paper has as main objective generalize solutions already known from general relativity to the $f(G)$ theory. To do that, we first correct some misprints of the Odintsov and Nojiri's work in order to introduce the formalism that will be used in the $f(G)$ gravity. In order to satisfy all field equations, the method to find solutions in alternative theories generates different $f(R)$ and $f(G)$ functions for each solution, where only the nonlinear term of $f(G)$ contributes to the field equations. We also analyze the energy conditions, since it is expected that some must be violated to find regular black holes, and using an auxiliary field, we analyze the nonlinearity of the electromagnetic theory., Comment: Published in PRD. 24 pages, 6 figures

In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case., Comment: 22 pages, 25 figures.Version published in EPJC

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work show that the Bardeen model may also be interpreted as a solutions of Einstein equations in the presence of a electric source, whose electric field does not behaves as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions., Comment: 9 pages, 8 figures

We show that there is an inconsistency in the class of solutions obtained in Phys. Rev. D {\bf 95}, 084037 (2017). This inconsistency is due to the approximate relation between lagrangian density and its derivative for Non-Linear Electrodynamics. We present an algorithm to obtain new classes of solutions., Comment: 3 pages

We study the generalization of the mass function of classes of regular spherically symmetric black holes solutions of in $ 4D $ coming from the coupling of General Relativity with Non-linear Electrodynamics, through the requirement of the energy conditions. Imposing that the solution must be regular and that the Weak and Dominant Energy Conditions are simultaneously satisfied, for models with the symmetry $T^0_{\;\;0} = T^1_{\;\;1} $ of the tensor energy-momentum, we construct a new general class of regular black holes of which two cases are asymptotically Reissner-Nordstrom., Comment: 12 pages, 1 figure, accepted for publication in JCAP

Cation ordering is most common process detected in A$_{3}$B'B"$_{2}$O$_{9}$-based complex perovskites. Some important physical features of this system are due to the B-site ordering at long and short range. For microwave applications as filters and resonators, the 1:2 order is more appropriate. Otherwise, the oxygen vacancies and 1:1 order are considered the main factors behind the good performance of nonstoichiometric A$_{3}$B'$_{1+x}$B"$_{2-x}$O$_{9-\delta}$-based ceramics as proton conductors. Until now, however, there are no available reports regarding the isolated effects of B-site order at long range on the electrical properties of stoichiometric systems. This work reports the preparation of 1:1 and 1:2 fully-ordered Ba$_{3}$CaNb$_{2}$O$_{9}$ ceramics. Here, we combine the Raman scattering and group-theory calculations to distinguish the fingerprints of the 1:1 and 1:2 orders. The electric properties of the ordered Ba$_{3}$CaNb$_{2}$O$_{9}$ are analyzed in terms of a phenomenological model based on a parallel combination of a resistor, constant phase element, and capacitor. In particular, the conductivity relaxation ascribed to the grain is due to the oxygen vacancies. Besides, we found that the 1:1 order increases the dc conductivity, but not enough to account the good performance reported for the non-stoichiometric Ba$_{3}$Ca$_{1+x}$Nb$_{2-x}$O$_{9-\delta}$-based proton conductors., Comment: 33 pages, 8 figures, 3 tables

Octahedral tilting is most common distortion process observed in centrosymmetric perovskite compounds (ABO$_{3}$). Indeed, crucial physical properties of this oxide stem from the tilts of BO$_{6}$ rigid octahedra. In microwave ceramics with perovskite-type structure, there is a close relation between the temperature coefficient of resonant frequency and tilt system of the perovskite structure. However, in many cases, limited access facilities are needed to assign correctly the space group, including neutron scattering and transmission electron microscopy. Here, we combine the Raman scattering and group-theory calculations to probe the structural distortion in the perovskite (Ba$_{1-x}$Sr$_{x}$)$_{3}$CaNb$_{2}$O$_{9}$ solid solution, which exhibits a structural phase transition at $x$ $\geq$ 0.7, from D$_{3d}^{3}$ trigonal to C$_{2h}^{3}$ monoclinic cell. Both phases are related by an octahedral tilting distortion ($a^{0}b^{-}b^{-}$ in Glazer notation). Low temperature Raman spectra corroborate the group-theoretical predictions for Sr$_{3}$CaNb$_{2}$O$_{9}$ compound, since 36 modes detected at 25 K agree well with those 42 (25A$_{g}$ $\oplus$ 17B$_{g}$) predicted ones., Comment: 21 pages, 5 figures, 1 table

We studied the spherical accretion of matter by charged black holes on $f(T)$ Gravity. Considering the accretion model of a isentropic perfect fluid we obtain the general form of the Hamiltonian and the dynamic system for the fluid. We have analysed the movements of an isothermal fluid model with $p=\omega e$ and where $p$ is the pressure and $e$ the total energy density. The analysis of the cases shows the possibility of spherical accretion of fluid by black holes, revealing new phenomena as cyclical movement inside the event horizon., Comment: 12 pages, revtex4 format. arXiv admin note: text overlap with arXiv:1503.07427, arXiv:1503.07857, arXiv:1509.03267, arXiv:1501.00621