Both the Galactic center and LRDs host million-solar-mass black holes within dense, cold reservoirs of molecular gas, and are electromagnetically tranquil. These conditions enable complex molecular chemistry and may serve as natural laboratories for prebiotic genetic evolution by allowing the synthesis of organic molecules essential for life.

A new version of the Teukolksy Master Equation, describing any massless field of different spin $s=1/2,1,3/2,2$ in the Kerr black hole, is presented here in the form of a wave equation containing additional curvature terms. These results suggest a relation between curvature perturbation theory in general relativity and the exact wave equations satisfied by the Weyl and the Maxwell tensors, known in the literature as the de Rham-Lichnerowicz Laplacian equations. We discuss these Laplacians both in the Newman-Penrose formalism and in the Geroch-Held-Penrose variant for an arbitrary vacuum spacetime. Perturbative expansion of these wave equations results in a recursive scheme valid for higher orders. This approach, apart from the obvious implications for the gravitational and electromagnetic wave propagation on a curved spacetime, explains and extends the results in the literature for perturbative analysis by clarifying their true origins in the exact theory.

Both the Galactic center and LRDs host million-solar-mass black holes within dense, cold reservoirs of molecular gas, and are electromagnetically tranquil. These conditions enable complex molecular chemistry and may serve as natural laboratories for prebiotic genetic evolution by allowing the synthesis of organic molecules essential for life.

We compute the binding energy and angular momentum of a test-particle at the last stable circular orbit (LSO) on the equatorial plane around a general relativistic, rotating neutron star (NS). We present simple, analytic, but accurate formulas for these quantities that fit the numerical results and which can be used in several astrophysical applications. We demonstrate the accuracy of these formulas for three different equations of state (EOS) based on nuclear relativistic mean-field theory models and argue that they should remain still valid for any NS EOS that satisfy current astrophysical constraints. We compare and contrast our numerical results with the corresponding ones for the Kerr metric characterized by the same mass and angular momentum.

The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background field is inhomogeneous and anisotropic in the former case, whereas it is inhomogeneous but isotropic in the latter. The features of light scattering are investigated by assuming the interaction region to be sandwiched between two flat spacetime regions, where light rays propagate along straight lines. Standard tools of ordinary wave optics are used to study the deflection of photon paths due to the interaction with the radiation fields, allowing for a comparison between the optical properties of the equivalent media associated with the different background fields.

We consider the interpretation of a pair of kHz Quasi Periodic Oscillations (QPOs) in the Fourier spectra of two Low Mass X-Ray Binaries, Sco X-1 and 4U1608-52, hosting an old accreting neutron star. The observed frequency difference of these QPOs decreaseas as their frequency increases, contrary to simple beat frequency models, which predict a constant frequency difference. We show that the behaviour of these QPOs is instead well matched in terms of the fundamental frequencies (in the radial and azimuthal directions) for test particle motion in the gravitational field of the neutron star, for reasonable star masses, and nearly independent of the star spin. The radial frequency must be much smaller than the azimuthal one, testifying that kHz QPOs are produced close to the innermost stable orbit. These results are not reproduced through the post--Newtonian (PN) approximation of General Relativity (GR). kHz QPOs from X-ray binaries likely provide an accurate laboratory for strong field GR.

A scalar field equivalent to a non-ideal "dark energy fluid" obeying a Shan-Chen-like equation of state is used as the background source of a flat Friedmann-Robertson-Walker cosmological spacetime to describe the inflationary epoch of our universe. Within the slow-roll approximation, a number of interesting features are presented, including the possibility to fulfill current observational constraints as well as a graceful exit mechanism from the inflationary epoch.

We have recently introduced a new model for the distribution of dark matter (DM) in galaxies based on a self-gravitating system of massive fermions at finite temperatures, the Ruffini-Argüelles-Rueda (RAR) model. We show that this model, for fermion masses in the keV range, explains the DM halo of the Galaxy and predicts the existence of a denser quantum core at the center. We demonstrate here that the introduction of a cutoff in the fermion phase-space distribution, necessary to account for the finite Galaxy size, defines a new solution with a central core which represents an alternative to the black hole (BH) scenario for SgrA*. For a fermion mass in the range $mc^2 = 48$ -- $345$~keV, the DM halo distribution is in agreement with the Milky Way rotation curve data, while harbors a dense quantum core of about $4\times10^6 M_\odot$ within the S2-star pericenter.

It has previously been discovered that there is a universal power law behavior exhibited by the late X-ray emission (LXRE) of a "golden sample" (GS) of six long energetic GRBs, when observed in the rest-frame of the source. This remarkable feature, independent of the different isotropic energy (E_iso) of each GRB, has been used to estimate the cosmological redshift of some long GRBs. This analysis is extended here to a new class of 161 long GRBs, all with E_iso > 10^52 erg. These GRBs are indicated as binary-driven hypernovae (BdHNe) in view of their progenitors: a tight binary system composed of a carbon-oxygen core (CO_core) and a neutron star undergoing an induced gravitational collapse (IGC) to a black hole triggered by the CO_core explosion as a supernova (SN). We confirm the universal behavior of the LXRE for the "enlarged sample" (ES) of 161 BdHNe observed up to the end of 2015, assuming a double-cone emitting region. We obtain a distribution of half-opening angles peaking at 17.62 degrees, with a mean value of 30.05 degrees, and a standard deviation of 19.65 degrees. This, in turn, leads to the possible establishment of a new cosmological candle. Within the IGC model, such universal LXRE behavior is only indirectly related to the GRB and originates from the SN ejecta, of a standard constant mass, being shocked by the GRB emission. The fulfillment of the universal relation in the LXRE and its independence of the prompt emission, further confirmed in this article, establishes a crucial test for any viable GRB model.

Within the binary-driven hypernova I (BdHN I) scenario, the gamma-ray burst GRB190114C originates in a binary system composed of a massive carbon-oxygen core (CO$_{core}$), and a binary neutron star (NS) companion. As the CO$_{core}$ undergoes a supernova explosion with the creation of a new neutron star ($\nu$NS), hypercritical accretion occurs onto the companion binary neutron star until it exceeds the critical mass for gravitational collapse. The formation of a black hole (BH) captures $10^{57}$ baryons by enclosing them within its horizon, and thus a cavity of approximately $10^{11}$ cm is formed around it with initial density $10^{-7}$ g/cm$^3$. A further depletion of baryons in the cavity originates from the expansion of the electron-positron-photon ($e^{+}e^{-}\gamma$) plasma formed at the collapse, reaching a density of $10^{-14}$ g/cm$^3$ by the end of the interaction. It is demonstrated here using an analytical model complemented by a hydrodynamical numerical simulation that part of the $e^{+}e^{-}\gamma$ plasma is reflected off the walls of the cavity. The consequent outflow and its observed properties are shown to coincide with the featureless emission occurring in a time interval of duration $t_{rf}$, measured in the rest frame of the source, between $11$ and $20$ s of the GBM observation. Moreover, similar features of the GRB light curve were previously observed in GRB 090926A and GRB 130427A, all belonging to the BdHN I class. This interpretation supports the general conceptual framework presented in Ruffini et al. (2019) and guarantees that a low baryon density is reached in the cavity, a necessary condition for the operation of the "inner engine" of the GRB presented in an accompanying article (Ruffini & Moradi 2019).

We analyze the extraction of the rotational energy of a Kerr black hole (BH) endowed with a test charge and surrounded by an external test magnetic field and ionized low-density matter. For a magnetic field parallel to the BH spin, electrons move outward (inward) and protons inward (outward) in a region around the BH poles (equator). For zero charge, the polar region comprises spherical polar angles $-60^\circ\lesssim \theta \lesssim 60^\circ$ and the equatorial region $60^\circ\lesssim \theta \lesssim 120^\circ$. The polar region shrinks for positive charge, and the equatorial region enlarges. For an isotropic particle density, we argue the BH could experience a cyclic behavior: starting from a zero charge, it accretes more polar protons than equatorial electrons, gaining net positive charge, energy, and angular momentum. Then, the shrinking(enlarging) of the polar(equatorial) region makes it accrete more equatorial electrons than polar protons, gaining net negative charge, energy, and angular momentum. In this phase, the BH rotational energy is extracted. The extraction process continues until the new enlargement of the polar region reverses the situation, and the cycle repeats. We show that this electrodynamical process produces a relatively limited increase of the BH irreducible mass compared to gravitational mechanisms like the Penrose process, hence being a more efficient and promising mechanism for extracting the BH rotational energy.

It was shown that pair luminosity of the newborn strange star with temperature of $10^{11}$ K may be as high as $L_\pm\simeq 10^{52}$ erg/s. The question remains: can a strange star maintain such a high surface temperature for a long time? To answer this question we studied thermal evolution of newborn strange star taking into account thermal conductivity of free quarks and neutrino emission by the URCA process. Our results show that extremely high luminosity due to the Schwinger process and insufficient thermal conductivity of quarks leads to development of steep temperature gradient at the surface of strange star. As a result, the temperature at the surface and hence its luminosity decreases as a power law, reaching $10^{40}$ erg/s already at 10 ms. This result holds even in the presence of neutrinosphere.

This article is based on the tutorial we gave at the hands-on workshop of the ICRANet-ISFAHAN Astronomy Meeting. We first introduce the basic theory of machine learning and sort out the whole process of training a neural network. We then demonstrate this process with an example of inferring redshifts from SDSS spectra. To emphasize that machine learning for astronomy is easy to get started, we demonstrate that the most basic CNN network can be used to obtain high accuracy, we also show that with simple modifications, the network can be converted for classification problems and also to processing gravitational wave data.

We use neural network algorithms for finding compression methods of images in the framework of iterated function systems which is a collection of the transformations of the interval $(0, 1)$ satisfying suitable properties.

The observation of a gamma-ray burst (GRB) associated with a supernova (SN) coincides remarkably with the energy output from a binary system comprising a very massive carbon-oxygen (CO) core and an associated binary neutron star (NS) by the Binary-Driven Hypernova (BdHN) model. The dragging effect in the late evolution of such systems leads to co-rotation, with binary periods on the order of minutes, resulting in a very fast rotating core and a binary NS companion at a distance of $\sim 10^5$ km. Such a fast-rotating CO core, stripped of its hydrogen and helium, undergoes gravitational collapse and, within a fraction of seconds, leads to a supernova (SN) and a newly born, fast-spinning neutron star ($\nu$NS), we name the emergence of the SN and the $\nu$NS as the SN-rise and $\nu$NS-rise. Typically, the SN energies range from $10^{51}$ to $10^{53}$ erg. We address this issue by examining 10 cases of Type-I BdHNe, the most energetic ones, in which SN accretion onto the companion NS leads to the formation of a black hole (BH). In all ten cases, the energetics of the SN events are estimated, ranging between $0.18$ and $12 \times 10^{52}$ erg. Additionally, in all 8 sources at redshift $z$ closer than $4.61$, a clear thermal blackbody component has been identified, with temperatures between $6.2$ and $39.99$ keV, as a possible signature of pair-driven SN. The triggering of the X-ray afterglow induced by the $\nu$NS-rise are identified in three cases at high redshift where early X-ray observations are achievable, benefits from the interplay of cosmological effects.

Gerbert of Aurillac wrote to Constantine of Fleury in 978 a letter to describe in detail the procedure to point the star nearest to the North celestial pole. This was made to align a sphere equipped with tubes to observe the celestial pole, the polar circles, the solstices and equinoxes. The use of tubes in astronomical observation is later reported by Alhazen in his treatise on optics (1011-1021). The description of pointing to the celestial pole indicates that the instrument must be accurately aligned with the true pole, materialized at that epoch by a star of fifth magnitude, at the limit of naked eye visibility, and then the instrument must remain fixed. Solstices and Equinoxes are points of the orbit of the Sun, so the sphere could be used as a tool for observing the Sun and probably determine the duration of the tropical year. This sphere was much more than a didactic tool, given the long procedure for the accurate alignement. Moreover "Rogatus a pluribus" (asked by his many students), Gerbert wrote a treatise on acoustic tubes (fistulae) in 980: Mensura Fistularum. He knew the difference in behavior of the fistulae compared with the acoustic strings, already studied by the Pythagoreans, and the treaty is intended to present the law that governs the length of the organ pipes in two octaves, compared to the corresponding acoustic strings. In terms of modern physics we know that acoustic tubes require an "end correction" to be tuned, which is proportional to the diameter of the tube. This proportionality is the same for every note. The mathematical law is simple, but Gerbert preferred to create a law in which the proportions of pipes and strings should be calculated through a series of fractions linked to the number 12 and its multiples.

Recently Usov's mechanism of pair creation on the surface of compact astrophysical objects has been revisited [1] with a conclusion that the pair creation rate was previously underestimated in the literature by nearly two orders of magnitude. Here we consider an alternative hypothesis of pair creation due to a perturbation of the surface of a compact object. Radial perturbation is induced in hydrodynamic velocity resulting in a microscopic displacement of the negatively charged component with respect to the positively charged one. The result depends on the ratio between the spatial scale of the perturbation $\lambda$ and the mean free path $l$. When $\lambda\sim l$ the perturbation energy is converted into a burst of electron-positron pairs which are created in collisionless plasma oscillations at the surface; after energy excess is dissipated electrosphere returns to its electrostatic configuration. When instead $\lambda\gg l$, the perturbation is thermalized, its energy is transformed into heat, and pairs are created continuously by the heated electrosphere. We discuss the relevant astrophysical scenarios.

The Dainotti relation empirically connects the isotropic plateau luminosity ($L_X$) in gamma-ray bursts (GRBs) X-ray afterglows to the rest-frame time at which the plateau ends ($T_a^*$), enabling both the standardization of GRBs and their use as cosmological probes. However, the precise physical mechanisms underlying this correlation remain an active area of research. Although magnetars, highly magnetized neutron stars, have been proposed as central engines powering GRB afterglows, traditional dipole spin-down radiation models fail to account for the full diversity of observed behaviors. This limitation necessitates a more comprehensive framework. We propose that multipolar magnetic field emissions from magnetars offer a plausible explanation for the Dainotti relation. Unlike simple dipole fields, higher-order multipolar configurations enable more complex energy dissipation processes. The coexistence of multiple components can plausibly explain the range of afterglow decay indices found from a sample of 238 GRBs with plateau features from the Swift-XRT database up to the end of December 2024, the majority of which deviate from the dipolar prediction of $\alpha = -2$, and more crucially, the spin-down physics yields a link between $L_X$ and $T_a^*$ in a way that preserves the Dainotti correlation with a slope of $b = - 1$, independent of the specific multipole order. Moreover, we find that the inclusion of higher order multipoles can explain the range of plateau energies found in the Dainotti relations. Thus, a unified picture emerges in which multipolar fields are able to reproduce both the slope and the normalization of the correlation.

By identifying the recently introduced Barbero-Immirzi field with the QCD axion, the strong CP problem can be solved through the Peccei-Quinn mechanism. A specific energy scale for the Peccei-Quinn symmetry breaking is naturally predicted by this model. This provides a complete dynamical setting to evaluate the contribution of such an axion to the cold dark matter content of the Universe. Furthermore, a tight upper bound on the tensor-to-scalar ratio production of primordial gravitational waves can be fixed, representing a strong experimental test for this model.

Strange quark stars (SQSs), namely compact stars entirely composed of deconfined quark matter, are characterized by similar masses and compactness to neutron stars (NSs) and have been theoretically proposed to exist in the Universe since the 1970s. However, multiwavelength observations of compact stars in the last 50 years have not yet led to an unambiguous SQS identification. This article explores whether SQSs could form in the supernova (SN) explosion of an evolved star (e.g., carbon-oxygen, or Wolf-Rayet) occurring in a binary with the companion being a neutron star (NS). The collapse of the iron core of the evolved star generates a newborn NS and the SN explosion. Part of the ejected matter accretes onto the NS companion as well as onto the newborn NS via matter fallback. The accretion occurs at hypercritical (highly super-Eddington) rates, transferring mass and angular momentum to the stars. We present numerical simulations of this scenario and demonstrate that the density increase in the NS interiors during the accretion process may induce quark matter deconfinement, suggesting the possibility of SQS formation. We discuss the astrophysical conditions under which such a transformation may occur and possible consequences.