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The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas analytic approximations to each individual solution within a numerical family have been proposed, proxies for whole families are missing, which can facilitate studying properties across the parameter space, data compression and a wider usage of such solutions. In this work we tackle this need, proposing a simple strategy based on a double expansion of the unknown functions in an appropriately chosen basis, to build such proxy. We use as an exploratory case-study spherical, fundamental mini-boson stars, to illustrate the feasibility of such an approach, emphasise its advantage in reducing the data size, and the challenges, say, in covering large parameter spaces., Comment: 27 pages, 9 figures

This work investigates the potential of Reinforcement Learning (RL) to tackle robot motion planning challenges in the dynamic RoboCup Small Size League (SSL). Using a heuristic control approach, we evaluate RL's effectiveness in obstacle-free and single-obstacle path-planning environments. Ablation studies reveal significant performance improvements. Our method achieved a 60% time gain in obstacle-free environments compared to baseline algorithms. Additionally, our findings demonstrated dynamic obstacle avoidance capabilities, adeptly navigating around moving blocks. These findings highlight the potential of RL to enhance robot motion planning in the challenging and unpredictable SSL environment., Comment: 12 pages, 3 figures, 3 tables

We analyse the lensing images by dynamically robust rotating (mini-)Proca stars surrounded by thin accretion disks. Due to their peculiar geodesic structure we show that these images exhibit striking similarities with the ones of BHs, for appropriately chosen disk intensity profile, when imposing a GRMHD-motivated emission cut off. Additionally, and unlike the non-rotating case, these similarities prevail even when considering equatorial observations. This example illustrates how a horizonless compact object without light rings, with a plausible formation mechanism and dynamically robust, could mimic detailed features of black hole imagiology., Comment: 23 pages, 11 figures + appendix

It has been established that Black Hole (BH) spacetimes obeying some general set of assumptions always possess, at least, one light ring (per rotation sense) [arXiv:2003.06445]. This theorem was originally established for asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular spacetimes harbouring a non-extremal and topologically spherical Killing horizon. Following the mantra that a theorem is only as strong as its assumptions in this work we extend this theorem to non topologically spherical (toroidal) BHs and to spacetimes harbouring more than one BH. As in [arXiv:2003.06445], we show that each BH still contributes with, at least, one LR (per rotation sense)., Comment: 17 pages, 9 figures

Skin lesions are classified in benign or malignant. Among the malignant, melanoma is a very aggressive cancer and the major cause of deaths. So, early diagnosis of skin cancer is very desired. In the last few years, there is a growing interest in computer aided diagnostic (CAD) using most image and clinical data of the lesion. These sources of information present limitations due to their inability to provide information of the molecular structure of the lesion. NIR spectroscopy may provide an alternative source of information to automated CAD of skin lesions. The most commonly used techniques and classification algorithms used in spectroscopy are Principal Component Analysis (PCA), Partial Least Squares - Discriminant Analysis (PLS-DA), and Support Vector Machines (SVM). Nonetheless, there is a growing interest in applying the modern techniques of machine and deep learning (MDL) to spectroscopy. One of the main limitations to apply MDL to spectroscopy is the lack of public datasets. Since there is no public dataset of NIR spectral data to skin lesions, as far as we know, an effort has been made and a new dataset named NIR-SC-UFES, has been collected, annotated and analyzed generating the gold-standard for classification of NIR spectral data to skin cancer. Next, the machine learning algorithms XGBoost, CatBoost, LightGBM, 1D-convolutional neural network (1D-CNN) were investigated to classify cancer and non-cancer skin lesions. Experimental results indicate the best performance obtained by LightGBM with pre-processing using standard normal variate (SNV), feature extraction providing values of 0.839 for balanced accuracy, 0.851 for recall, 0.852 for precision, and 0.850 for F-score. The obtained results indicate the first steps in CAD of skin lesions aiming the automated triage of patients with skin lesions in vivo using NIR spectral data.

The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable., Comment: To be submitted to journal. Comments are welcome

We present radio observations of 24 confirmed and candidate strongly lensed quasars identified by the Gaia Gravitational Lenses (GraL) working group. We detect radio emission from 8 systems in 5.5 and 9 GHz observations with the Australia Telescope Compact Array (ATCA), and 12 systems in 6 GHz observations with the Karl G. Jansky Very Large Array (VLA). The resolution of our ATCA observations is insufficient to resolve the radio emission into multiple lensed images, but we do detect multiple images from 11 VLA targets. We have analysed these systems using our observations in conjunction with existing optical measurements, including measuring offsets between the radio and optical positions, for each image and building updated lens models. These observations significantly expand the existing sample of lensed radio quasars, suggest that most lensed systems are detectable at radio wavelengths with targeted observations, and demonstrate the feasibility of population studies with high resolution radio imaging.

Within nonlinear electrodynamics (NED), photons follow null geodesics of an effective geometry, which is different from the geometry of the spacetime itself. Over the last years, several works were dedicated to investigate the motion of photons in the effective geometry of NED-based magnetically charged regular black hole (RBH) solutions. However, there are few works considering electrically charged RBHs. We study the light rings, shadows, and gravitational lensing of the electrically charged RBH solution proposed by Irina Dymnikova (ID), which is a static and spherically symmetric spacetime with a NED source. We show that the shadow associated to the effective geometry can be almost 10% bigger that the one associated to the standard geometry. We also find that the ID solution may mimic the shadow properties of the Reissner-Nordstr\"om (RN) BH, for low-to-extreme values of the electric charge. Besides that, by using the backwards ray-tracing technique, we obtain that ID and RN BH solutions can have a very similar gravitational lensing, for some values of the correspondent electric charges. We also show that the motion of photons in the effective geometry can be interpreted as a non-geodesic curve submitted to a 4-force term, from the perspective of an observer in the standard geometry., Comment: 16 pages, 13 figures

Lean Six Sigma (LSS) is a comprehensive and powerful strategy for processes improvement and products. There is a cornucopia of tools for its implementation and 37 among them were selected to carry out an evaluation based on three factors, namely: Frequency of use of the tool, difficulty in implementing, importance and impact of the tool in the implementation of LSS. An online survey was conducted with Portuguese consultants and it included questions on the profile, and the companies they worked, as well as the degree of impact of the tools used. Consultants were asked to choose ten tools, ranking them in order of importance. The frequencies with which each tool had been cited were counted. A procedure was then developed to identify the know-how of consultants to establish a ranking of LSS tools. It was created an ordering list of tools, which emphasized in: Honshin Kanri, VOC, VSM. The results presented are particularly relevant when is considered the importance of understanding the requirements for a successful implementation of Lean Six Sigma management system in the organizations., Comment: 7 pages, 3 figures, 1 table

We investigate the gravitational lensing by spinning Proca stars and the shadows and lensing by Kerr black holes (BHs) with synchronised Proca hair, discussing both theoretical aspects and observational constraints from the Event Horizon Telescope (EHT) M87* and Sgr A* data. On the theoretical side, this family of BHs interpolates between Kerr-like solutions -- exhibiting a similar optical appearance to that of Kerr BHs -- to very non-Kerr like solutions, exhibiting exotic features such as cuspy shadows, egg-like shadows and ghost shadows. We interpret these features in terms of the structure of the fundamental photon orbits, for which different branches exist, containing both stable and unstable orbits, with some of the latter not being shadow related. On the observational side, we show that current EHT constraints are compatible with all such BHs that could form from the growth of the superradiant instability of Kerr BHs. Unexpectedly, given the (roughly) 10% error bars in the EHT data -- and in contrast to their scalar cousin model --, some of the BHs with up to 40% of their energy in their Proca hair are compatible with the current data. We estimate the necessary resolution of future observations to better constrain this model., Comment: 36 pages, 20 figures + appendix

The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this paper we resort to auxiliary 2-dimensional metrics to study circular geodesics of generic static, spherically symmetric, and asymptotically flat $1 + 3$ dimensional spacetimes, whose functions are at least $C^2$ smooth. This is done by studying the Gaussian curvature of the bidimensional equivalent manifold as well as the geodesic curvature of circular paths on these. This study considers both null and timelike circular geodesics. The study of null geodesics through the optical manifold retrieves the known result of the number of light rings (LRs) on the spacetime outside a black hole and on spacetimes with horizonless compact objects. With an equivalent procedure we can formulate a similar theorem on the number of marginally stable timelike circular orbits (TCOs) of a given spacetime satisfying the previously mentioned assumption, Comment: 7 pages + Appendices

Ultracompact objects with light-rings (LRs) but without an event horizon could mimic black holes (BHs) in their strong gravity phenomenology. But are such objects dynamically viable? Stationary and axisymmetric ultracompact objects that can form from smooth, quasi-Minkowski initial data must have at least one stable LR, which has been argued to trigger a spacetime instability; but its development and fate have been unknown. Using fully non-linear numerical evolutions of ultracompact bosonic stars free of any other known instabilities and introducing a novel adiabatic effective potential technique, we confirm the LRs triggered instability, identifying two possible fates: migration to non-ultracompact configurations or collapse to BHs. In concrete examples we show that typical migration/collapse time scales are not larger than $\sim 10^3$ light-crossing times, unless the stable LR potential well is very shallow. Our results show that the LR instability is effective in destroying horizonless ultracompact objects that could be plausible BH imitators., Comment: 5 pages + Appendices; Videos can be found in this URL http://gravitation.web.ua.pt/node/3889; v2. Title changed per request of journal. Published in Physical Review Letters as Editor's Suggestion and Featured in Physics

The light rings (LRs) topological charge (TC) of a spacetime measures the number of stable LRs minus the number of unstable LRs. It is invariant under smooth spacetime deformations obeying fixed boundary conditions. Asymptotically flat equilibrium black holes (BHs) have, generically, TC=$-1$. In Einstein-Maxwell theory, however, the Schwarzschild-Melvin BH - describing a neutral BH immersed in a strong magnetic field - has TC$=0$. This allows the existence of BHs without LRs and produces remarkable phenomenological features, like panoramic shadows. Here we investigate the generalised Schwarzschild-Melvin solution in Einstein-Maxwell-dilaton theory, scanning the effect of the dilaton coupling $a$. We find that the TC changes discontinuously from TC$=0$ to TC$=-1$ precisely at the Kaluza-Klein value $a=\sqrt{3}$, when the (empty) Melvin solution corresponds to a twisted Kaluza-Klein reduction of five-dimensional flat spacetime, $i.e.$ the dilaton coupling $a$ induces a topological transition in the TC. We relate this qualitative change to the Melvin asymptotics for different $a$. We also study the shadows and lensing of the generalised Schwarzschild-Melvin solution for different values of $a$, relating them to the TC.

Active Galactic Nuclei (AGN) are relevant sources of radiation that might have helped reionising the Universe during its early epochs. The super-massive black holes (SMBHs) they host helped accreting material and emitting large amounts of energy into the medium. Recent studies have shown that, for epochs earlier than $z~{\sim}~5$, the number density of SMBHs is on the order of few hundreds per square degree. Latest observations place this value below $300$ SMBHs at $z~{\gtrsim}~6$ for the full sky. To overcome this gap, it is necessary to detect large numbers of sources at the earliest epochs. Given the large areas needed to detect such quantities, using traditional redshift determination techniques -- spectroscopic and photometric redshift -- is no longer an efficient task. Machine Learning (ML) might help obtaining precise redshift for large samples in a fraction of the time used by other methods. We have developed and implemented an ML model which can predict redshift values for WISE-detected AGN in the HETDEX Spring Field. We obtained a median prediction error of $\sigma_{z}^{N} = 1.48 \times (z_{\mathrm{Predicted}} - z_{{\mathrm{True}}}) / (1 + z_{\mathrm{True}}) = 0.1162$ and an outlier fraction of $\eta = 11.58 \%$ at $(z_{\mathrm{Predicted}} - z_{{\mathrm{True}}}) / (1 + z_{\mathrm{True}}) > 0.15$, in line with previous applications of ML to AGN. We also applied the model to data from the Stripe 82 area obtaining a prediction error of $\sigma_{z}^{N} = 0.2501$., Comment: 15 pages, 5 figures. Accepted to the Special Issue "A New Window on the Radio Emission from Galaxies, Galaxy Clusters and Cosmic Web: Current Status and Perspectives" of MDPI Galaxies

We investigate the null geodesic flow and in particular the light rings (LRs), fundamental photon orbits (FPOs) and shadows of a black hole (BH) immersed in a strong, uniform magnetic field, described by the Schwarzschilld-Melvin electrovacuum solution. The empty Melvin magnetic Universe contains a tube of planar LRs. Including a BH, for weak magnetic fields, the shadow becomes oblate, whereas the intrinsic horizon geometry becomes prolate. For strong magnetic fields (over-critical solutions), there are no LRs outside the BH horizon, a result explained using topological arguments. This feature, together with the light confining structure of the Melvin Universe yields \textit{panoramic shadows}, seen (almost) all around the equator of the observer's sky. Despite the lack of LRs, there are FPOs, including polar planar ones, which define the shadow edge. We also observe and discuss chaotic lensing, including in the empty Melvin Universe, and multiple disconnected shadows., Comment: Matches the version published in Physical Review D, typos corrected, 17 pages, 11 figures

We consider the following question: may two different black holes (BHs) cast exactly the same shadow? In spherical symmetry, we show the necessary and sufficient condition for a static BH to be shadow-degenerate with Schwarzschild is that the dominant photonsphere of both has the same impact parameter, when corrected for the (potentially) different redshift of comparable observers in the different spacetimes. Such shadow-degenerate geometries are classified into two classes. The first shadow-equivalent class contains metrics whose constant (areal) radius hypersurfaces are isometric to those of the Schwarzschild geometry, which is illustrated by the Simpson and Visser (SV) metric. The second shadow-degenerate class contains spacetimes with different redshift profiles and an explicit family of metrics within this class is presented. In the stationary, axi-symmetric case, we determine a sufficient condition for the metric to be shadow degenerate with Kerr for far-away observers. Again we provide two classes of examples. The first class contains metrics whose constant (Boyer-Lindquist-like) radius hypersurfaces are isometric to those of the Kerr geometry, which is illustrated by a rotating generalization of the SV metric, obtained by a modified Newman-Janis algorithm. The second class of examples pertains BHs that fail to have the standard north-south $\mathbb{Z}_2$ symmetry, but nonetheless remain shadow degenerate with Kerr. The latter provides a sharp illustration that the shadow is not a probe of the horizon geometry. These examples illustrate that nonisometric BH spacetimes can cast the same shadow, albeit the lensing is generically different., Comment: Matches the version published in Physical Review D, title changed, typos corrected, 16 pages, 8 figures

Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact - i.e., possess LRs - but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions are considered. However, an effective shadow can arise in a different way: if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike geodesics (located at $r_{\rm ISCO}=6M$ for a Schwarzschild BH of mass M), the accretion flow morphology around BHs is mimicked and an effective shadow arises in an astrophysical environment. Even though spherical BSs may accommodate stable timelike circular orbits all the way down to their centre, we show the angular velocity along such orbits may have a maximum away from the origin, at $R_{\Omega}$; this scale was recently observed to mimic the BH's ISCO in some scenarios of accretion flow. Then: (i) for free scalar fields or with quartic self-interactions, $R_{\Omega}\neq 0$ only for perturbatively unstable BSs; (ii) for higher scalar self-interactions, e.g. axionic, $R_{\Omega}\neq 0$ is possible for perturbatively stable BSs, but no solution with $R_{\Omega}=6M$ was found in the parameter space explored; (iii) but for free vector fields, yielding Proca stars (PSs), perturbatively stable solutions with $R_{\Omega}\neq 0$ exist, and indeed $R_{\Omega}=6M$ for a particular solution. Thus, dynamically robust spherical PSs can mimic the shadow of a (near-)equilibrium Schwarzschild BH with the same M, in an astrophysical environment, despite the absence of a LR, at least under some observation conditions, as we confirm by comparing the lensing of such PSs and Schwarzschild BHs., Comment: Abstract abridged due to arXiv length limit; 22 pages, 9 figures

Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman-Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer-Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman-Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer-Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton-Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton-Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA., Comment: Published in The European Physical Journal C

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colours. It is expected, however, that at certain scales new physics, in particular in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr-Newman solution, and the other within the context of low-energy heterotic string theory, the Kerr-Sen solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions., Comment: 11 pages, 11 figures, Contribution to Selected Papers of the Fifth Amazonian Symposium on Physics, v2: references added, v3: typos corrected, matches published version

The ringdown and shadow of the astrophysically significant Kerr Black Hole (BH) are both intimately connected to a special set of bound null orbits known as Light Rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this letter we prove the following theorem. A stationary, axi-symmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a non-extremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes $C^2$-smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultra-compact object must admit an even number of non-degenerate LRs, one of which is stable., Comment: 5 pages, 3 figures

We consider a static, axially symmetric spacetime describing the superposition of a Schwarzschild black hole (BH) with a thin and heavy accretion disk. The BH-disk configuration is a solution of the Einstein field equations within the Weyl class. The disk is sourced by a distributional energy-momentum tensor and it is located at the equatorial plane. It can be interpreted as two streams of counter-rotating particles, yielding a total vanishing angular momentum. The phenomenology of the composed system depends on two parameters: the fraction of the total mass in the disk, $m$, and the location of the inner edge of the disk, $a$. We start by determining the sub-region of the space of parameters wherein the solution is physical, by requiring the velocity of the disk particles to be sub-luminal and real. Then, we study the null geodesic flow by performing backwards ray-tracing under two scenarios. In the first scenario the composed system is illuminated by the disk and in the second scenario the composed system is illuminated by a far-away celestial sphere. Both cases show that, as $m$ grows, the shadow becomes more prolate. Additionally, the first scenario makes clear that as $m$ grows, for fixed $a$, the geometrically thin disk appears optically enlarged, i.e., thicker, when observed from the equatorial plane. This is to due to light rays that are bent towards the disk, when backwards ray traced. In the second scenario, these light rays can cross the disk (which is assumed to be transparent) and may oscillate up to a few times before reaching the far away celestial sphere. Consequently, an almost equatorial observer sees different patches of the sky near the equatorial plane, as a chaotic "mirage". As $m\rightarrow 0$ one recovers the standard test, i.e., negligible mass, disk appearance., Comment: 24 pages, 15 figures