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We investigate the stability of scalar perturbations around a magnetized stationary compact object in General Relativity. The considered object is one of the simplest exact solutions of Einstein electrovacuum equations corresponding to a spheroidal body endowed with a dipole magnetic moment. It is effectively constructed by imposing a perfect reflection (mirror) boundary condition on a central region of the Gutsunaev-Manko spacetime. A time-domain analysis of the perturbations reveals a quasinormal phase followed by a power-law decaying tail. Our findings suggest that the exterior region of the magnetized compact object is stable in the entire parameter space. Moreover, the system tends to become generically more stable the stronger the magnetization of the central object is. Such findings can be useful for the qualitative understanding of more realistic astrophysical situations involving highly magnetized sources., Comment: 10 pages, 5 figures

In the present work, evaporation of a black hole immersed in a de Sitter environment is considered. Vaidya-de Sitter spacetime is used to model the process in a scenario of accelerated expansion of the Universe. The role of observers is highlighted in the development and Hayward thermodynamics for non stationary geometries is employed in the description of the compact objects. The results of the proposed dynamical model are compared with the usual description based on stationary geometries, focusing on primordial black holes (PBHs). It is found how the timescale of evaporation depends on the choice of a cosmological observer. It may differ substantially from the treatment based on stationary models for black holes. In particular, the standard assertion that there is a fixed initial mass just below $10^{15} \, \text{g} \sim 10^{-18} M_\odot$ for the PBHs which are ending their evaporation process today is imprecise, even when possible quantum corrections at the late stages are not considered. Deviations from this prediction appear when the evaporation is measured with respect to the cosmological time., Comment: 16 pages, 10 figures

In the present work we study the construction of different thermodynamic descriptions for the Kerr-anti-de Sitter (KadS) black holes. The early versions of the KadS thermodynamics are briefly discussed, highlighting some of its strong points and shortcomings. Isohomogeneous transformations, a procedure for generating new thermodynamics, are presented and geometrically interpreted for KadS. This tool is used to determine possible KadS thermodynamics that can be constructed to satisfy a Smarr formula, and the validity of the first law in the generated thermodynamics. The connection between new thermodynamic theories and early Hawking's approach is considered. In this new framework, the usual KadS thermodynamics is complemented with its geometric construction, and Hawking's proposal, which does not satisfy the first law, is improved to an alternative thermodynamic theory. With the quantum statistical relation, Hawking's and this alternative KadS thermodynamics are also generalized from four to higher dimensions., Comment: 16 pages. Accepted for publication in Physical Review D

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in $JHK_{\rm s}$ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took $\sim 2000$ hours, covering about 4% of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_{\rm s}$ catalogue of $\gtrsim 1.5\times10^9$ point sources, as well as a $K_{\rm s}$ band catalogue of $\sim 10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST., Comment: 17 pages, 11 figures (+ appendix). Accepted for publication in Astronomy and Astrophysics in section 14: Catalogs and data

In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the electromagnetic field in a finite $d$-dimensional box within a semi-classical treatment. In this context, corrections to the Stefan-Boltzmann law are obtained. Special attention is given to the two-dimensional scenario, since it can be used in the characterization of experimental setups. Another application concerns acoustic perturbations in a quasithermodynamic generalization of Debye model for a finite solid in d dimensions. Extensions and corrections for known results and usual formulas, such as the Debye frequency and Dulong-Petit law, are calculated., Comment: 21 pages, 2 figures. To be published in Journal of Physics A

Coaching is a complex endeavor that blends a myriad of concepts and skills. Practical experience, content knowledge, and coaching knowledge are instrumental to becoming an effective math coach. In order to design a professional development system to best support and build the capacity of coaches, we must identify what specific content and coaching knowledge is needed to become an effective coach. While there is a great deal of literature specifying coaching knowledge generally, for math coaches, it is critical to have a content-specific target within their professional learning. There are various types of knowledge, specific to math coaches, that are important to consider in relation to both coaching and content. This resource from Region 7CC examines some limitations of current mathematics instruction and provides key considerations for coaches of mathematics teachers.

Primordial black holes are analytically and numerically discussed based on the extended McVittie spacetime solution. By assuming that dark matter and radiation are the only sources of energy accreted by the forming central object, it is found that the black-hole mass evolution depends on the initial mass of the seed, the time in which the black hole emerges, and also on the average peculiar velocity of dark matter particles. Constraints on the initial conditions of the primordial black holes are derived from profiles of the black-hole accretion mechanism and cosmological environment. A large range of masses is compatible with our approach. In particular, masses of the order of $10^{10}M_{\odot}$ today may also be generated from small seeds. An incubation time for the emerging horizons is observed when the initial masses of the seeds are close to the particle-horizon mass. It is also argued that the McVittie-type description is consistent with the Schwarzschild solution as long as other astrophysical processes near the central object are neglected., Comment: 14 pages, 8 figures

In this work, we present an extensive dynamical analysis of the null geodesics in the spacetimes proposed by Casadio, Fabbri, and Mazzacurati (CFM), which model black holes and wormholes in a Randall-Sundrum brane. Geodesic stability is evaluated by Lyapunov and Jacobi criteria, with coinciding results. Semistable photon spheres are found in the geometries of interest. Bifurcations associated with the dynamical system are also investigated, characterizing a degenerated Bogdanov-Takens bifurcation. Our results suggest deep connections between the geometric characteristics of the CFM spacetimes and the dynamics of null geodesics in these backgrounds., Comment: 15 pages, 5 figures

In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed. The experimental viability of the proposal is studied within a specific context. We suggest that the main theoretical results developed in the present work could be experimentally verified., Comment: 19 pages, 1 figure

Autonomous Vehicles (AV) are expected to bring considerable benefits to society, such as traffic optimization and accidents reduction. They rely heavily on advances in many Artificial Intelligence (AI) approaches and techniques. However, while some researchers in this field believe AI is the core element to enhance safety, others believe AI imposes new challenges to assure the safety of these new AI-based systems and applications. In this non-convergent context, this paper presents a systematic literature review to paint a clear picture of the state of the art of the literature in AI on AV safety. Based on an initial sample of 4870 retrieved papers, 59 studies were selected as the result of the selection criteria detailed in the paper. The shortlisted studies were then mapped into six categories to answer the proposed research questions. An AV system model was proposed and applied to orient the discussions about the SLR findings. As a main result, we have reinforced our preliminary observation about the necessity of considering a serious safety agenda for the future studies on AI-based AV systems., Comment: 32 pages, 5 figures, 9 Tables

We report the detection of variable stars within a 11.5' x 11.5' region near the Galactic centre (GC) that includes the Arches and Quintuplet clusters, as revealed by the VISTA Variables in the Via Lactea (VVV) survey. There are 353 sources that show Ks-band variability, of which the large majority (81%) correspond to red giant stars, mostly in the asymptotic giant branch (AGB) phase. We analyze a population of 52 red giants with long-term trends that cannot be classified into the typical pulsating star categories. Distances and extinctions are calculated for 9 Mira variables, and we discuss the impact of the chosen extinction law on the derived distances. We also report the presence of 48 new identified young stellar object (YSO) candidates in the region., Comment: Resubmitted to MNRAS after a positive referee report, 21 pages, 23 figures and 3 tables

In this work we study a homogeneous and quasilocal Thermodynamics associated to the Schwarzschild-anti de Sitter black hole. The usual thermodynamic description is extended within a Hamiltonian approach with the introduction of the cosmological constant in the thermodynamic phase space. The treatment presented is consistent in as much as it respects the laws of black hole Thermodynamics and accepts the introduction of any thermodynamic potential. We are able to construct new equations of state that characterize the Thermodynamics. Novel phenomena can be expected from the proposed setup., Comment: 16 pages

We analyze the thermodynamics of massless bosonic systems in D-dimensional anti-de Sitter spacetime, considering scalar, electromagnetic, and gravitational fields. Their dynamics are described by Poschl-Teller effective potentials and quantized in a unified framework, with the determination of the associated energy spectra. From the microscopic description developed, a macroscopic thermodynamic treatment is proposed, where an effective volume in anti-de Sitter geometry is defined and a suitable thermodynamic limit is considered. Partition functions are constructed for the bosonic gases, allowing the determination of several thermodynamic quantities of interest. With the obtained results, general aspects of the thermodynamics are explored., Comment: 25 pages, 10 figures, published version

Using algebraic techniques we obtain quasinormal modes and frequencies associated to generalized forms of the scattering P\"oschl-Teller potential. This approach is based on the association of the corresponding equations of motion with Casimir invariants of differential representations of the Lie algebra sl(2). In the presented development, highest weight representations are constructed and fundamental states are calculated. An infinite tower of quasinormal mode solutions is obtained by the action of a lowering operator. The algebraic results are used in the analysis of the Cauchy initial value problem associated to the generalized P\"oschl-Teller potentials. For the scattering potentials considered, there are no late-time tails and the dynamics is always stable., Comment: 14 pages, 2 figures. Accepted for publication in Classical and Quantum Gravity

In this work we study the Thermodynamics of D-dimensional Schwarzschild-anti de Sitter (SAdS) black holes. The minimal Thermodynamics of the SAdS spacetime is briefly discussed, highlighting some of its strong points and shortcomings. The minimal SAdS Thermodynamics is extended within a Hamiltonian approach, by means of the introduction of an additional degree of freedom. We demonstrate that the cosmological constant can be introduced in the thermodynamic description of the SAdS black hole with a canonical transformation of the Schwarzschild problem, closely related to the introduction of an anti-de Sitter thermodynamic volume. The treatment presented is consistent, in the sense that it is compatible with the introduction of new thermodynamic potentials, and respects the laws of black hole Thermodynamics. By demanding homogeneity of the thermodynamic variables, we are able to construct a new equation of state that completely characterizes the Thermodynamics of SAdS black holes. The treatment naturally generates phenomenological constants that can be associated with different boundary conditions in underlying microscopic theories. A whole new set of phenomena can be expected from the proposed generalization of SAdS Thermodynamics., Comment: 13 pages, published version

The Quintuplet cluster is one of the most massive star clusters in the Milky Way, situated very close to the Galactic center. We present a new search for variable stars in the vicinity of the cluster, using the five-year database of the Vista Variables in the Via Lactea (VVV) ESO Public Survey in the near-infrared. A total of 7586 objects were identified in the zone around $2'$ from the cluster center, using 55 $K_S$-band epochs. Thirty-three stars show $K_S$-band variability, 24 of them being previously undiscovered. Most of the variable stars found are slow/semiregular variables, long-period variables of the Mira type, and OH/IR stars. In addition, a good number of our candidates show variations in a rather short timescale. We also propose four Young Stellar Object (YSO) candidates, which could be cluster members., Comment: 14 pages, 10 figures. Accepted for publication in MNRAS

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac's theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases., Comment: 11 pages, published version

In this work we consider electromagnetic dynamics in Randall-Sundrum branes. It is derived a family of four-dimensional spacetimes compatible with Randall-Sundrum brane worlds, focusing on asymptotic flat backgrounds. Maximal extensions of the solutions are constructed and their causal structures are discussed. These spacetimes include singular, non-singular and extreme black holes. Maxwell's electromagnetic field is introduced and its evolution is studied in an extensive numerical survey. Electromagnetic quasinormal mode spectra are derived and analyzed with time-dependent and high-order WKB methods. Our results indicate that the black holes in the brane are electromagnetically stable., Comment: 12 pages, 12 figures, published version

We present the discovery of 816 high amplitude infrared variable stars ($\Delta K_{\rm s} >$ 1 mag) in 119 deg$^2$ of the Galactic midplane covered by the Vista Variables in the Via Lactea (VVV) survey. Almost all are new discoveries and about 50$\%$ are YSOs. This provides further evidence that YSOs are the commonest high amplitude infrared variable stars in the Galactic plane. In the 2010-2014 time series of likely YSOs we find that the amplitude of variability increases towards younger evolutionary classes (class I and flat-spectrum sources) except on short timescales ($<$25 days) where this trend is reversed. Dividing the likely YSOs by light curve morphology, we find 106 with eruptive light curves, 45 dippers, 39 faders, 24 eclipsing binaries, 65 long-term periodic variables (P$>$100 days) and 162 short-term variables. Eruptive YSOs and faders tend to have the highest amplitudes and eruptive systems have the reddest SEDs. Follow up spectroscopy in a companion paper verifies high accretion rates in the eruptive systems. Variable extinction is disfavoured by the 2 epochs of colour data. These discoveries increase the number of eruptive variable YSOs by a factor of at least 5, most being at earlier stages of evolution than the known FUor and EXor types. We find that eruptive variability is at least an order of magnitude more common in class I YSOs than class II YSOs. Typical outburst durations are 1 to 4 years, between those of EXors and FUors. They occur in 3 to 6\% of class I YSOs over a 4 year time span., Comment: Accepted for publication in MNRAS, 51 pages, 23 figures