It is well known that the electrically charged Reissner-Nordstr\"{o}m black hole could be overcharged. Here, we investigate the process of overcharging of a magnetized Reissner-Nordstr\"{o}m black hole that includes effect of the magnetic field generated by own magnetic charge of source on the background geometry. It is found that magnetic field prevents a transition to occur from black hole to naked singularity, thus overcharging cannot be attained which happens due to the fact that the magnetic field reaches its threshold value. It turns out that beyond threshold value the magnetic field can exert large Lorentz force on particles and dominate over the gravitational force, allowing charged particles not to fall into the black hole. One may conclude, there occurs no evidence for violation of cosmic censorship conjecture for a magnetized Reissner-Nordstr\"{o}m black hole beyond threshold value of the magnetic field.

We study a binary Bose gas in a symmetric dual-core, pancake-shaped trap, modelled by two linearly coupled two-dimensional Gross-Pitaevskii equations with Lee-Huang-Yang corrections. Two different cases are considered. First, we consider a spatially uniform condensate, where we identify the domains of parameters for macroscopic quantum tunnelling, self-trapping and localisation revivals. The analytical formulas for the Josephson frequencies in the zero- and $\pi$-phase modes are derived. As the total atom number varies, the system displays a rich bifurcation structure. In the zero-phase, two successive pitchfork bifurcations generate bistability and hysteresis, while the $\pi$-phase exhibits a single pitchfork bifurcation. The second case is when the quantum droplets are in a dual-core trap. Analytical predictions for the oscillation frequencies are derived via a variational approach for the coupled dynamics of quantum droplets, and direct numerical simulations validate the results. We identify critical values of the linear coupling that separate Josephson and self-trapped regimes as the particle number changes. We also found the Andreev-Bashkin superfluid drag effect in numerical simulations of the droplet-droplet interactions in the two-core geometry.

In this work, we prove that the complement of the Brjuno set in $\mathbb{C}^n$ has zero $C_\sigma$-capacity with respect to the kernel $k_\sigma(z,\xi)=\|z-\xi\|^{-2n+2}|\log{\|z-\xi\||^{\sigma}}$ for any $\sigma>n$. In particular, it follows that it has zero $h_\delta$-Hausdorff measure with respect to the $h_\delta(t)=t^{2n-2}|\log{t}|^{-\delta}$, for any $\delta>n+1$. This generalizes a previous result of Sadullaev and the second author in dimension one to higher dimensions.

In this letter, we present a novel analytical Schwarzschild-like black hole (BH) solution that exhibits a static BH with a dark matter (DM) halo characterized by a Dehnen-type density profile. We study the properties of the newly derived BH solution by examining its spacetime curvature characteristics and energy conditions, providing insights into how the DM halo influences these fundamental characteristics. This solution could represent an alternative perspective on the interaction of black hole-dark matter systems, providing new insights into the fundamental properties of DM halos.

Hydrogen is considered an alternative source of energy to fossil fuels for the fulfilment of current energy demands. Photocatalysis initiates the hydrogen evolution reaction which is believed to be the greenest approach to produce hydrogen through clean, safe, and environmentally friendly methods. In this Review, we focus mainly on the comprehensive analysis of the 2D and 3D bulk materials on the basis of their superior photocatalytic activities. However, several literatures have reported the superiority of 2D material over the bulk counterpart in terms of photocatalytic performance owing to their ultrathin layered structures, offer a higher surface-to-volume ratio, flexibility, large active sites for incoming H2O molecules, etc. We have thoroughly analysed the drawbacks of various hydrogen production methods focusing on the photocatalysis mechanism and the processes of evolution of hydrogen. In addition to this, a short overview of the various solid-state materials for photocatalysis that have been developed so far and their mechanisms are discussed. Lastly, we have discussed the recent developments in 2D materials and their composites as promising photocatalysts.

We address the equilibrium configurations and stability properties of anisotropic compact stars whose interior is described by a modified Chaplygin gas (MCG) equation of state in the framework of the regularized four-dimensional Einstein-Gauss-Bonnet (4DEGB) theory. Applying a quasi-local prescription for the pressure anisotropy, we derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations and integrate them numerically over a large parameter space in the Gauss-Bonnet coupling $\alpha$ and the degree of anisotropy $\beta$. We provide mass-radius sequences, mass-compactness, energy density, and pressure profiles, and perform a full stability analysis based on the turning-point criterion, the radial adiabatic index $\gamma_r$, and the radial and transverse sound speeds $v_r^2$ and $v_t^2$. Our results show that positive $\alpha$ and positive anisotropy $(\beta > 0)$ systematically increase the maximum mass and radius, enabling then configurations that exceed $2\,M_\odot$ while still obeying causality and the modified Buchdahl bound in 4DEGB gravity. A comparison with the latest astrophysical constraints (NICER, GW170817, GW190814, and massive-pulsar measurements) identifies regions of the $(\alpha,\beta)$ parameter space that are observationally allowable. In conclusion, anisotropic dark-energy stars in 4DEGB gravity provide viable, observationally testable ultra-compact alternatives to normal neutron stars and black holes, and also potentially open rich avenues for further multi-messenger searches for higher-curvature effects.

The nuclear transient AT2019cuk/Tick Tock/SDSS J1430+2303 has been suggested to harbor a supermassive black hole (SMBH) binary near coalescence. We report results from high-cadence NICER X-ray monitoring with multiple visits per day from January-August 2022, as well as continued optical monitoring during the same time period. We find no evidence of periodic/quasi-periodic modulation in the X-ray, UV, or optical bands, however we do observe exotic hard X-ray variability that is unusual for a typical AGN. The most striking feature of the NICER light curve is repetitive hard (2-4 keV) X-ray flares that result in distinctly harder X-ray spectra compared to the non-flaring data. In its non-flaring state, AT2019cuk looks like a relatively standard AGN, but it presents the first case of day-long, hard X-ray flares in a changing-look AGN. We consider a few different models for the driving mechanism of these hard X-ray flares, including: (1) corona/jet variability driven by increased magnetic activity, (2) variable obscuration, and (3) self-lensing from the potential secondary SMBH. We prefer the variable corona model, as the obscuration model requires rather contrived timescales and the self-lensing model is difficult to reconcile with a lack of clear periodicity in the flares. These findings illustrate how important high-cadence X-ray monitoring is to our understanding of the rapid variability of the X-ray corona and necessitate further high-cadence, multi-wavelength monitoring of changing-look AGN like AT2019cuk to probe the corona-jet connection.

The history of the quadratic stochastic operators can be traced back to work of this http URL (1924). During more than 80 years this theory developed and many papers were published. In recent years it has again become of interest in connection with numerous applications to many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems.

We present extensive photometric and spectroscopic observations of the peculiar Type Ia supernova (SN Ia) 2022vqz. It shares many similarities with the SN 2002es-like SNe Ia, such as low luminosity ($M_{B,\rm max}=-18.11\pm0.16$ mag) and moderate post-peak decline rate ($\Delta m_{15,B}=1.33\pm0.11$ mag). The nickel mass synthesised in the explosion is estimated as $0.20\pm0.04~{\rm M}_\odot$ from the bolometric light curve, which is obviously lower than that of normal SNe Ia. SN 2022vqz is also characterised by slowly expanding ejecta, with Si II velocities persisting around 7000 km s$^{-1}$ since 16 days before peak brightness, unique among all known SNe Ia. While all of these properties imply a lower-energy thermonuclear explosion that should leave a considerable amount of unburnt materials, the absent signature of unburnt carbon in spectra of SN 2022vqz is puzzling. A prominent early peak is clearly detected in the ATLAS $c$- and $o$-band light curves and in the ZTF $gr$-band data within days after the explosion. Possible mechanisms for the early peak are discussed, including the sub-Chandrasekhar-mass double-detonation model and interaction of SN ejecta with circumstellar material. We find that both models face some difficulties in replicating all aspects of the observed data. As an alternative, we propose a hybrid C-O-Ne white dwarf as the progenitor of SN 2022vqz; it can simultaneously reconcile the tension between low ejecta velocity and the absence of carbon. We further discuss the diversity of SN 2002es-like objects and their origin in the context of different scenarios.

In this work, we study the gravitational waveforms from the periodic orbits of a massive particle around a dyonic ModMax black hole. We begin with a brief analysis of the spacetime and then examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. In particular, we compute the characteristics of marginally bound orbits and innermost stable circular orbits. Our results show that the values of these quantities increase with the black hole charge $Q$ and the screening parameter $\gamma$. We then plot various periodic orbits, characterized by the integers ($z$,$w$,$v$). Finally, we present the gravitational waveforms associated with extreme mass ratio inspirals, consisting of a stellar-mass compact object orbiting a supermassive black hole.

In this study, using the Dirac continuum model combined with the split-operator technique, we investigate the propagation dynamics of wave packets in graphene in the presence of circular potential barriers arranged in square and triangular geometries. Our results reveal a non-monotonic dependence of the wave packet transmission on the number of barrier rows along the propagation direction: the transmission initially decreases as rows of barriers are removed, but then increases again when additional rows are eliminated. To explain the observed nonlinear behavior, the time evolution of the transmission probability is analyzed, providing insight into the interplay between wave packet dynamics and the spatial arrangement of potential barriers. These findings offer a pathway for designing graphene-based devices with tunable transport properties through engineered potential landscapes.

The nuclear transient AT2019cuk/Tick Tock/SDSS J1430+2303 has been suggested to harbor a supermassive black hole (SMBH) binary near coalescence. We report results from high-cadence NICER X-ray monitoring with multiple visits per day from January-August 2022, as well as continued optical monitoring during the same time period. We find no evidence of periodic/quasi-periodic modulation in the X-ray, UV, or optical bands, however we do observe exotic hard X-ray variability that is unusual for a typical AGN. The most striking feature of the NICER light curve is repetitive hard (2-4 keV) X-ray flares that result in distinctly harder X-ray spectra compared to the non-flaring data. In its non-flaring state, AT2019cuk looks like a relatively standard AGN, but it presents the first case of day-long, hard X-ray flares in a changing-look AGN. We consider a few different models for the driving mechanism of these hard X-ray flares, including: (1) corona/jet variability driven by increased magnetic activity, (2) variable obscuration, and (3) self-lensing from the potential secondary SMBH. We prefer the variable corona model, as the obscuration model requires rather contrived timescales and the self-lensing model is difficult to reconcile with a lack of clear periodicity in the flares. These findings illustrate how important high-cadence X-ray monitoring is to our understanding of the rapid variability of the X-ray corona and necessitate further high-cadence, multi-wavelength monitoring of changing-look AGN like AT2019cuk to probe the corona-jet connection.

We study a binary Bose gas in a symmetric dual-core, pancake-shaped trap, modelled by two linearly coupled two-dimensional Gross-Pitaevskii equations with Lee-Huang-Yang corrections. Two different cases are considered. First, we consider a spatially uniform condensate, where we identify the domains of parameters for macroscopic quantum tunnelling, self-trapping and localisation revivals. The analytical formulas for the Josephson frequencies in the zero- and $\pi$-phase modes are derived. As the total atom number varies, the system displays a rich bifurcation structure. In the zero-phase, two successive pitchfork bifurcations generate bistability and hysteresis, while the $\pi$-phase exhibits a single pitchfork bifurcation. The second case is when the quantum droplets are in a dual-core trap. Analytical predictions for the oscillation frequencies are derived via a variational approach for the coupled dynamics of quantum droplets, and direct numerical simulations validate the results. We identify critical values of the linear coupling that separate Josephson and self-trapped regimes as the particle number changes. We also found the Andreev-Bashkin superfluid drag effect in numerical simulations of the droplet-droplet interactions in the two-core geometry.

Superluminous supernovae are among the most energetic stellar explosions in the Universe, but their energy sources remain an open question. Here we present long-term observations of one of the closest examples of the hydrogen-poor subclass (SLSNe-I), SN~2017egm, revealing the most complicated known luminosity evolution of SLSNe-I. Three distinct post-peak bumps were recorded in its light curve collected at about $100$--350\,days after maximum brightness, challenging current popular power models such as magnetar, fallback accretion, and interaction between ejecta and a circumstellar shell. However, the complex light curve can be well modelled by successive interactions with multiple circumstellar shells with a total mass of about $6.8$--7.7\,M$_\odot$. In this scenario, large energy deposition from interaction-induced reverse shocks results in ionization of neutral oxygen in the supernova ejecta and hence a much lower nebular-phase line ratio of [O\,\textsc{i}] $\lambda6300$/([Ca\,\textsc{ii}] + [O\,\textsc{ii}]) $\lambda7300$ ($\sim 0.2$) compared with that derived for other superluminous and normal stripped-envelope SNe. The pre-existing multiple shells indicate that the progenitor of SN~2017egm experienced pulsational mass ejections triggered by pair instability within 2 years before explosion, in robust agreement with theoretical predictions for a pre-pulsation helium-core mass of 48--51\,M$_{\odot}$. Finally, this work shows that the final explosion product may be a black hole with about 40\,M$_{\odot}$, and has significant implication for the formation of such heavy black holes that have been recently observed by LIGO-Virgo gravitational wave detectors.

In this work, we investigated the motion of spinning test particles around a rotating wormhole, extending, in this way, the previous work of Benavides-Gallego et al. in [Phys. Rev. D 101, no.12, 124024] to the general case. Using the Mathisson-Papapetrous-Dixon equations, we study the effective potential, circular orbits, and the innermost stable circular orbit (ISCO) of spinning test particles. We found that both the particle and wormhole spins affect the location of the ISCO significantly. On the other hand, Similar to the non-rotating case, we also found two possible configurations in the effective potential: plus and minus. Furthermore, the minimum value of the effective potential is not at the throat due to its spin, in contrast to the motion of the non-spinning test particles in a non-rotating wormhole, where the effective potential is symmetric, and its minimum value is at the throat. In the case of the ISCO, we found that it increases as the spin of the wormhole a increases, in contrast to black holes where the presence of spin decreases the value of the ISCO. Finally, since the dynamical four-momentum and kinematical four-velocity of the spinning particle are not always parallel, we consider the superluminal bound, finding that the allowed values of s change as the wormhole's spin a increases.

In this paper, we have investigated the dynamics of magnetized particles around 4-D Einstein-Gauss-Bonnet black hole immersed in an external asymptotically uniform magnetic field. We have shown that the magnetic interaction parameter responsible for circular orbits decreases for negative values of the Gauss-Bonnet parameter $\alpha$ and the range where magnetized particle's stable circular orbits are allowed increases for the positive values of the parameter $\alpha$. The study of the collisions of magnetized, charged and neutral particles has shown that the center-of-mass energy of the particles increases in the presence of positive Gauss-Bonnet parameter. Finally, we show how the magnetic interaction and Gauss-Bonnet parameter may mimic the effect of rotation of the Kerr black hole giving the same ISCO radius for magnetized particles. Detailed analysis of the ISCO show that spin of Kerr black hole can not be mimicked by the effects of magnetic interaction and the Gauss-Bonnet parameters when \alpha<-4.37 and the spin parameter a > 0.237.

This work is devoted to study the effects of Einstein-\AE ther gravity on the dynamics of magnetized particles orbiting a static, spherically symmetric and uncharged black hole immersed in an external asymptotically uniform magnetic field in both comoving and proper observers frames. The analysis is carried out by varying the free parameters $c_{13}$ and $c_{14}$ of the Einstein-\AE ther theory and noticing their impacts on the particle trajectories, radii of the innermost stable circular orbits (ISCOs), and the amount of center-of-mass energy produced as a result of the collision. The strength of the magnetic field and the location of circular orbits is significantly affected by varying the above free parameters. We have also made detailed comparisons between the effects of parameters of Einstein-\AE ther and spin of rotating Kerr black holes on ISCO followed by magnetized particles and noticed that both black holes depict similar behaviour for suitable values of $c_{13}$, $c_{14}$, spin and the magnetic coupling parameters which provide exactly the same values for the ISCO. Finally, we have analysed the cases when a static \AE ther black hole can be described as Schwarzschild black hole in modified gravity (MOG) with the corresponding values of the parameters of the black holes.

A very unique strength of the Devasthal Observatory is its capability of detecting optical transients with the 4-m International Liquid Mirror Telescope (ILMT) and to rapidly follow them up using the 1.3-m Devasthal Fast Optical Telescope (DFOT) and/or the 3.6-m Devasthal Optical Telescope (DOT), installed right next to it. In this context, we have inspected 20 fields observed during 9 consecutive nights in October-November 2022 during the first commissioning phase of the ILMT. Each of these fields has an angular extent of $22^\prime$ in declination by $9 \times 22^\prime$ in right ascension. Combining both a visual search for optical transients and an automatic search for these using an image subtraction technique (see the ILMT poster paper by Pranshu et al.), we report a total of 232 significant transient candidates. After consulting the Minor Planet Center database of asteroids, we could identify among these 219 positions of known asteroids brighter than $V=22$. These correspond to the confirmed positions of 78 distinct known asteroids. Analysis of the remaining CCD frames covering 19 more fields (out of 20) should lead to an impressive number of asteroids observed in only 9 nights. The conclusion is that in order to detect and characterize new supernovae, micro-lensing events, highly variable stars, multiply imaged quasars, etc. among the ILMT optical transients, we shall first have to identify all known and new asteroids. Thanks to its large diameter and short focal length (f/D $\sim$ 2.4), the ILMT turns out to be an excellent asteroid hunter.

In the era of sky surveys like Palomar Transient Factory (PTF), Zwicky Transient Facility (ZTF) and the upcoming Vera Rubin Observatory (VRO) and ILMT, a plethora of image data will be available. ZTF scans the sky with a field of view of 48 deg$^{2}$ and VRO will have a FoV of 9.6 deg$^{2}$ but with a much larger aperture. The 4m ILMT covers a 22$'$ wide strip of the sky. Being a zenith telescope, ILMT has several advantages like low observation air mass, best image quality, minimum light pollution and no pointing time loss. Transient detection requires all these imaging data to be processed through a Difference Imaging Algorithm (DIA) followed by subsequent identification and classification of transients. The ILMT is also expected to discover several known and unknown astrophysical objects including transients. Here, we propose a pipeline with an image subtraction algorithm and a convolutional neural network (CNN) based automated transient discovery and classification system. The pipeline was tested on ILMT data and the transients as well as variable candidates were recovered and classified.