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In this work, we study a static, spherically charged AdS black hole within a modified cosmological Chaplygin gas (MCG), adhering to the calorific equation of state, as a unified dark fluid model of dark energy and dark matter. We explore the influence of model parameters on several characteristics of the MCG-motivated charged AdS black hole (MCG-AdSBH), including the geodesic structure and some astrophysical phenomena such as null trajectories, shadow silhouettes, light deflection angles, and the determination of greybody bounds. We then discuss how the model parameters affect the Hawking temperature, remnant radius, and evaporation process of the MCG-AdSBH. Quasinormal modes are also investigated using the eikonal approximation method. Constraints on the MCG-AdSBH parameters are derived from EHT observations of M87* and Sgr A*, suggesting that MCG-AdSBH could be strong candidates for astrophysical black hole., Comment: 8 pages, 11 figures, 4 tables

Motivated by the effect of the energy of moving particles in $C-$metric, we first obtain exact accelerating black hole solutions in gravity's rainbow. Then, we study the effects of gravity's rainbow and $C-$metric parameters on the Ricci and Kretschmann scalars, and also the asymptotical behavior of this solution. Next, we indicate how different parameters of the obtained accelerating black holes in gravity's rainbow affect thermodynamics quantities (such as the Hawking temperature, and entropy) and the local stability (by evaluating the heat capacity). In the following, we extract the geodesic equations to determine the effects of various parameters on photon trajectory in the vicinity of this black hole, as well as obtain the radius of the photon sphere and the corresponding critical impact parameter to gain insight into AdS black hole physics by adding the gravity's rainbow to $C-$metric., Comment: 12 pages, 4 figures, 1 table

This work explores various manifestations of bumblebee gravity within the metric-affine formalism. We investigate the impact of the Lorentz violation parameter, denoted as $X$, on the modification of the Hawking temperature. Our calculations reveal that as $X$ increases, the values of the Hawking temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the quasinormal modes, we employ the WKB method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz-violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the quasinormal spectrum on time-dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time-domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of $X$ correspond to larger shadow radii. Furthermore, we constrain the magnitude of the shadow radii using the EHT horizon-scale image of $Sgr A^*$. Finally, we calculate both the time delay and the deflection angle., Comment: 32 pages, 8 figures and 4 tables

This work investigates several key aspects of a non--commutative theory with mass deformation. We calculate thermodynamic properties of the system and compare our results with recent literature. We examine the \textit{quasinormal} modes of massless scalar perturbations using two approaches: the WKB approximation and the P\"oschl--Teller fitting method. Our results indicate that stronger non--commutative parameters lead to slower damping oscillations of gravitational waves and higher partial absorption cross sections. Furthermore, we study the geodesics of massless and massive particles, highlighting that the non--commutative parameter $\Theta$ significantly impacts the paths of light and event horizons. Also, we calculate the shadows, which show that larger values of $\Theta$ correspond to larger shadow radii. Finally, we explore the deflection angle and time delay in this context., Comment: 35 pages, 10 figures

The effects of dark matter spike in the vicinity of the supermassive black hole, located at the center of M87 (the Virgo A galaxy), are investigated within the framework of the so-called Bumblebee Gravity. Our primary aim is to determine whether the background of spontaneous Lorentz symmetry breaking has a significant effect on the horizon, ergo-region, and shadow of the Kerr Bumblebee black hole in the spike region. For this purpose, we first incorporate the dark matter distribution in a Lorentz-violating spherically symmetric space-time as a component of the energy-momentum tensors in the Einstein field equations. This leads to a space-time metric for a Schwarzschild Bumblebee black hole with a dark matter distribution in the spike region and beyond. Subsequently, this solution is generalized to a Kerr Bumblebee black hole through the use of the Newman-Janis-Azreg-A\"inou algorithm. Then, according to the available observational data for the dark matter spike density and radius, and the Schwarzschild radius of the supermassive black hole in Virgo A galaxy, we examine the shapes of shadow and demonstrate the influence of the spin parameter $a$, the Lorentz-violating parameter $\ell$ and the corresponding dark matter halo parameters $\rho_{0}$ and $r_{0}$ on the deformation and size of the shadow., Comment: accepted for publication in JCAP

In this work, we study the thermodynamic properties on a non--commutative background via gravitational gauge field potentials. This procedure is accomplished after contracting de Sitter (dS) group, $\mathrm{SO}(4,1)$, with the Poincar\`e group, $\mathrm{ISO}(3,1)$. Particularly, we focus on a static spherically symmetric black hole. In this manner, we calculate the modified Hawking temperature and the other deformed thermal state quantities, namely, entropy, heat capacity, Helmholtz free energy and pressure. Finally, we also investigate the black hole evaporation process in such a context., Comment: 14 pages

In this study, we investigated the influence of the topological defects space-time with a spiral dislocation on a spin-zero boson field by using the Duffin-Kemmer-Petiau (DKP) equation. To be more specific, we solved the generalized spin-zero DKP equation in the presence of a spiral dislocation exactly. We derived the wave function and corresponding energy eigenvalues for two cases, in the absence and presence of a static potential by using analytical methods. We numerically demonstrated the effect of the spiral dislocation on the solutions., Comment: 14 Pages, 4 figures

In this study, we considered a moving particle with a magnetic quadrupole moment in an elastic medium in the presence of a screw dislocation. We assumed a radial electric field in a rotating frame that leads a uniform effective magnetic field perpendicular to the plane of motion. We solved the Schr\"odinger equation to derive wave and energy eigenvalue functions by employing analytical methods for two interaction configurations: in the absence of potential and in the presence of a static scalar potential. Due to the topological defect in the medium, we observed a shift in the angular momentum quantum number which affects the energy eigenvalues and the wave function of the system., Comment: 12 pages, 7 figures

In this contribution, we investigate the interaction between electric and magnetic fields with an electric quadrupole moment of a spinless particle moving in an elastic medium which has a topological defect (screw dislocation). By considering this interaction, the Schr\"odinger equation is exactly solved by using the analytical method. Thus, the eigenfunction and energy eigenvalues for two configurations are found. Meanwhile, by observing a shift in the angular momentum quantum number, the energy eigenvalues and the wave function of the system are modified, due to the screw dislocation in the medium., Comment: 6 pages, 3 figures

A graph G is called well-indumatched if all of its maximal induced matchings have the same size. In this paper we characterize all well-indumatched trees. We provide a linear time algorithm to decide if a tree is well-indumatched or not. Then, we characterize minimal well-indumatched graphs of girth at least 9 and show subsequently that for an odd integer g greater than or equal to 9 and different from 11, there is no well-indumatched graph of girth g. On the other hand, there are infinitely many well-indumatched unicyclic graphs of girth k, where k is in {3, 5, 7} or k is an even integer greater than 2. We also show that, although the recognition of well-indumatched graphs is known to be co-NP-complete in general, one can recognize in polynomial time well-indumatched graphs where the size of maximal induced matchings is fixed.

In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent Schrodinger equation and It is also noted that these wave functions are sensitive to variation in the parameters involved., Comment: Accepted for publishing in Advances in High Energy Physics journal

In this paper we use the Nikiforv-Uvarov method to obtain the approximate solutions of the Klein-Gordon equation with deformed five parameter exponential type potential (DFPEP) model. We also obtain the solutions of the Schr\"odinger equation in the presence of the DFPEP in the non-relativistic limits. In addition, we calculate in the nonrelativistic limits the thermodynamics properties such as vibrational mean energy U, free energy F and the specific heat capacity C . Special cases of the potential are also discussed., Comment: 29 pages, 14 figures, 1 table

In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can be easily solved analytically through separation of variables. The energy eigenvalues and the normalization constant of the radial wave functions are obtained, as well as the scattering phase shifts., Comment: 10 pages, Latex, accepted in Journal-Korean Physical Society (JKPS)

We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the reflection and transmission coefficients by making use of the matching conditions on the wave functions. The effect of position dependent mass on the reflection and transmission coefficients of the system is duly investigated., Comment: 14 pages, 4 figures, accepted in Eur. Phys. J. Plus. arXiv admin note: text overlap with arXiv:1204.6562 by other authors

Let G=(V,E) be a simple undirected graph. For a given set L of the real line, a function omega from E to L is called an L-flow. Given a vector gamma whose coordinates are indexed by V, we say that omega is a gamma-L-flow if for each v in V, the sum of the values on the edges incident to v is gamma(v). If gamma(v)=c, for all v in V, then the gamma-L-flow is called a c-sum L-flow. In this paper we study the existence of gamma-L-flows for various choices of sets L of real numbers, with an emphasis on 1-sum flows. Given a natural k number, a c-sum k-flow is a c-sum flow with values from the set {-1,1,...,1-k, k-1}. Let L be a subset of real numbers containing 0 and let L* be L minus 0 by L*. Answering a question from a recent paper we characterize which bipartite graphs admit a 1-sum R*-flow or a 1-sum Z*-flow. We also show that that every k-regular graph, with k either odd or congruent to 2 modulo 4, admits a 1-sum {-1, 0, 1}-flow., Comment: 20 pages, 1 figure

Let $G$ be a graph. A zero-sum flow in $G$ is an assignment of nonzero real number to the edges such that the sum of the values of all edges incident with each vertex is zero. Let $k$ be naturel number. A zero-sum $k$-flow is a flow with value from the set $\{\pm 1, \pm 2,..., \pm(k-1)\}$. It has been conjectured that every $r$-regular graph, $r\geq 3$, admits a zero-sum 5-flow. In this paper we give an affirmative answer to this conjecture, exept for r=5.

The energy of a graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. Let $G$ be a graph of order $n$ and ${\rm rank}(G)$ be the rank of the adjacency matrix of $G$. In this paper we characterize all graphs with $E(G)={\rm rank}(G)$. Among other results we show that apart from a few families of graphs, $E(G)\geq 2\max(\chi(G), n-\chi(\bar{G}))$, where $n$ is the number of vertices of $G$, $\bar{G}$ and $\chi(G)$ are the complement and the chromatic number of $G$, respectively. Moreover some new lower bounds for $E(G)$ in terms of ${\rm rank}(G)$ are given., Comment: Accepted for publication in Discrete Mathematics