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In this paper, we investigate the numerical solutions for spherically symmetric situations in Einstein cubic gravity. In addition to the previously found black hole solutions, we uncover a new class of solutions that lack horizons. Due to the divergence of the central curvature, these solutions represent a novel type of naked singularity. By varying parameters, we find that under certain conditions, the metric function can approach zero infinitely, indicating the emergence of a critical event horizon. These solutions, featuring a critical horizon and obtained solely from pure gravity model, can be described as frozen gravitational stars (FGSs). Additionally, the radius of this horizon is linked to the coupling constant lambda, increasing as lambda increases. Remarkably, from the perspective of an external observer, these solutions closely resemble extreme black holes. Notably, we find that for all values of lambda, the position of this critical horizon coincides with that of a Schwarzschild black hole of the same mass., Comment: 13 pages, 5 figures

In this paper, we construct a static spherical symmetric Bardeen-Dirac Stars (BDSs) in the four-dimensional Anti-de Sitter (AdS) spacetime, which consists of the electromagnetic field and Dirac field coupled to gravity. We investigate the ADM mass, Noether charge and light rings of BDSs in AdS spacetime. In asymptotically Minkowski spacetime, the maximum frequency of BDSs is one. However, we observe that the maximum frequency of BDSs increases as the cosmological constant decreases in AdS spacetime. Additionally, BDSs can exhibit extreme behavior at low frequencies, refer to as Frozen Bardeen-Dirac stars (FBDSs) in AdS spacetime. FBDSs have a critical event horizon, where the metric function gtt is very close to zero. The matter is entirely encapsulated by this critical horizon, highly concentrated within it. When the magnetic charge is fixed, the FBDSs gradually disappear as the cosmological constant decreases., Comment: 21 pages, 8 figures, 1 table

The DArk Matter Particle Explorer (DAMPE) is a satellite-borne particle detector for measurements of high-energy cosmic rays and {\gamma}-rays. DAMPE has been operating smoothly in space for more than 8 years since launch on December 17, 2015. The trigger logic of DAMPE is designed according to the deposited energy information recorded by the calorimeter. The precise calibration of the trigger thresholds and their long-term evolutions are very important for the scientific analysis of DAMPE. In this work, we develop a new method for the threshold calibration, considering the influence from the electronic noise, and obtain the long-term evolutions of the trigger thresholds. The average increase rate of the trigger thresholds for the first 4 layers of the calorimeter is found to be about 0.9% per year, resulting in variations of the high-energy trigger efficiency of cosmic ray electrons by about -5% per year at 2 GeV and less than about -0.05% above 30 GeV., Comment: 11 pages, 11 figures

In this work, we investigate a static spherically symmetric system in which Einstein gravity is minimally coupled with a self-interacting complex scalar field and a nonlinear electromagnetic field, referred to as Hayward axion stars. Employing numerical methods, we find that it essentially describes axion stars with the magnetic charge. In the absence of magnetic charge and with only the scalar field present, the system reduces to axion stars. We discover that when the magnetic charge $q$ exceeds a critical value, extreme solutions with frequencies $\omega$ approaching zero can be found and the critical horizon emerges. Within this horizon, the scalar field and energy density are highly concentrated and decrease precipitously at its boundary. The time component of the metric function approaches zero within this region, indicating that gravity is extremely intense, and time nearly ceases to flow. To an observer at infinity, the star appears to be frozen, hence we refer to these extreme solutions exhibiting a critical horizon as Hayward axion frozen stars. Furthermore, it is important to note that as $\omega \rightarrow 0$, the mass of the Hayward axion frozen star becomes independent of the decay constant and is only determined by the magnetic charge. Additionally, we find that the frozen star solutions possess two light rings. With an increase in the magnetic charge, these light rings move outward, while changes in the decay constant have little effect on their positions., Comment: 26 pages, 10 figures

Recently, Ref. \cite{Wang:2023tdz} investigated the model of Einstein-Bardeen theory coupled to a free complex scalar field. The introduction of the scalar field prevents the formation of the event horizon, and when the magnetic charge exceeds a certain critical value, the frozen Bardeen-boson star can be obtained with the frequency $\omega \rightarrow 0$. In this paper, we extend the investigation of the Einstein-Bardeen model with a charged scalar field and obtain two types of solutions: the small $q$ solution and the large $q$ solution. Specifically, for the small $q$ solution, we find that there exists a maximum value for the charge $q$, the introduction of the charge makes it possible to obtain solutions for frozen stars without the frequency to be approached to zero. For the large $q$ solution, the charge can tend toward infinity, and as $q \rightarrow \infty$, the large $q$ solution gradually becomes the pure Bardeen solution. Similar to Ref. \cite{Wang:2023tdz}, the event horizon is not found in our results., Comment: 20 pages, 6 figures

In this paper, we present the spherically symmetric wormhole in Einstein's gravity coupling phantom field and nonlinear electromagnetic field. Numerical results show that this solution violates the Null Energy Condition (NEC), and as the parameters change, the ADM mass of the entire spacetime changes from positive to negative. In addition, we analyze the light ring (LR) of the solution and demonstrate the astronomical observation properties. Especially when negative mass appears, the general LR will not appear, only a ``special unstable LR" exists at the throat, which is caused by the repulsive effect of the negative mass on both sides of the wormhole. Finally, we draw the embedding diagram to reflect the geometric characteristics of the wormhole., Comment: 21 pages, 8 figures. arXiv admin note: text overlap with arXiv:2311.17557

In this paper, we present a solution for a five-dimensional boson star under gravity with infinite tower of higher curvature corrections. We discover that when the coupling constant exceeds a certain threshold, an alternative configuration emerges, distinct from the conventional five-dimensional boson star. This new structure is characterized by a broader frequency range, with its minimum value approaching zero. At a truncation of $n=2$ for the correction order, the solution and its scalar curvature diverge as the frequency approaches zero. However, as the order of higher curvature corrections increases, the singularity at the center vanishes, resulting in a globally regular solution. Additionally, as the frequency approaches zero, the scalar field's radial distribution becomes concentrated within the critical radius $r_c$, forming what we term a ``frozen star". Beyond this radius, the metric of the frozen star almost degenerates into that of an extreme black hole. The solutions for such frozen stars offer a new avenue for exploring the enigmatic interiors of compact celestial bodies, enhancing our understanding of the internal structure of black holes under semi-classical conditions and potentially addressing the series of paradoxes associated with information loss due to singularities and horizons., Comment: 19 pages, 8 figures

Thanks to the application of deep learning technology in point cloud processing of the remote sensing field, point cloud segmentation has become a research hotspot in recent years, which can be applied to real-world 3D, smart cities, and other fields. Although existing solutions have made unprecedented progress, they ignore the inherent characteristics of point clouds in remote sensing fields that are strictly arranged according to latitude, longitude, and altitude, which brings great convenience to the segmentation of point clouds in remote sensing fields. To consider this property cleverly, we propose novel convolution operators, termed Twin Deformable point Convolutions (TDConvs), which aim to achieve adaptive feature learning by learning deformable sampling points in the latitude-longitude plane and altitude direction, respectively. First, to model the characteristics of the latitude-longitude plane, we propose a Cylinder-wise Deformable point Convolution (CyDConv) operator, which generates a two-dimensional cylinder map by constructing a cylinder-like grid in the latitude-longitude direction. Furthermore, to better integrate the features of the latitude-longitude plane and the spatial geometric features, we perform a multi-scale fusion of the extracted latitude-longitude features and spatial geometric features, and realize it through the aggregation of adjacent point features of different scales. In addition, a Sphere-wise Deformable point Convolution (SpDConv) operator is introduced to adaptively offset the sampling points in three-dimensional space by constructing a sphere grid structure, aiming at modeling the characteristics in the altitude direction. Experiments on existing popular benchmarks conclude that our TDConvs achieve the best segmentation performance, surpassing the existing state-of-the-art methods.

Research on multi-view stereo based on remote sensing images has promoted the development of large-scale urban 3D reconstruction. However, remote sensing multi-view image data suffers from the problems of occlusion and uneven brightness between views during acquisition, which leads to the problem of blurred details in depth estimation. To solve the above problem, we re-examine the deformable learning method in the Multi-View Stereo task and propose a novel paradigm based on view Space and Depth deformable Learning (SDL-MVS), aiming to learn deformable interactions of features in different view spaces and deformably model the depth ranges and intervals to enable high accurate depth estimation. Specifically, to solve the problem of view noise caused by occlusion and uneven brightness, we propose a Progressive Space deformable Sampling (PSS) mechanism, which performs deformable learning of sampling points in the 3D frustum space and the 2D image space in a progressive manner to embed source features to the reference feature adaptively. To further optimize the depth, we introduce Depth Hypothesis deformable Discretization (DHD), which achieves precise positioning of the depth prior by adaptively adjusting the depth range hypothesis and performing deformable discretization of the depth interval hypothesis. Finally, our SDL-MVS achieves explicit modeling of occlusion and uneven brightness faced in multi-view stereo through the deformable learning paradigm of view space and depth, achieving accurate multi-view depth estimation. Extensive experiments on LuoJia-MVS and WHU datasets show that our SDL-MVS reaches state-of-the-art performance. It is worth noting that our SDL-MVS achieves an MAE error of 0.086, an accuracy of 98.9% for <0.6m, and 98.9% for <3-interval on the LuoJia-MVS dataset under the premise of three views as input.

In this paper, we extend Chandrasekhar's method of calculating rotating black holes into $f(R)$ theory. We consider the Ricci scalar is a constant and derive the Kerr and Kerr-Ads metric by using the analytical mathematical method. Suppose that the spacetime is a 4-dimensional Riemannian manifold with a general stationary axisymmetric metric, we calculate Cartan's equation of structure and derive the Einstein tensor. In order to reduce the solving difficulty, we fix the gauge freedom to transform the metric into a more symmetric form. We solve the field equations in the two cases of the Ricci scalar $R=0$ and $R\neq 0$. In the case of $R=0$, the Ernst's equations are derived. We give the elementary solution of Ernst's equations and show the way to obtain more solutions including Kerr metric. In the case of $R\neq 0$, we reasonably assume that the solution to the equations consists of two parts: the first is Kerr part and the second is introduced by the Ricci scalar. Giving solution to the second part and combining the two parts, we obtain the Kerr-Ads metric. The calculations are carried out in a general $f(R)$ theory, indicating the Kerr and Kerr-Ads black holes exist widely in general $f(R)$ models. Furthermore, the whole solving process can be treated as a standard calculation procedure to obtain rotating black holes, which can be applied to other modified gravities.

In this paper, we study the spherically symmetric traversable wormholes with a scalar field supported by a phantom field in the anti-de Sitter (AdS) asymptotic spacetime. Despite coupling the scalar matter field, these wormholes remain massless and symmetric for reflection of the radial coordinate $r \rightarrow -r$. The solution possesses a finite Noether charge $Q$, which varies as a function of frequency $\omega$ with changes in the cosmological constant $\Lambda$ and the throat size $r_0$. Under specific conditions, an approximate ``event horizon'' will appear at the throat., Comment: 23 pages, 8 figures

In this paper, we construct the Dirac stars model composed of two Dirac fields and Einstein gravity in four-dimensional Anti-de Sitter spacetime. We consider the Dirac stars with free field (no self-interacting). Our investigation focuses on understanding the relationship between Arnowitt-Deser-Misner (ADM) mass, Noether charge, and binding energy in relation to the cosmological constant. Furthermore, we extend the study to the Dirac stars with self-interacting potentials. For the self-interacting Dirac stars, three types of interactions are examined: only quartic, only sextic, quartic and sextic interactions that is kind of Q-ball type interactions. In these three distinct scenarios, it is essential to investigate the impact of self-interaction constants on Dirac stars. Additionally, we study the Dirac Q-balls in the AdS background., Comment: 17pages, 27pictures

In this article, we investigate the stationary, soliton-like solutions in the model of the Einstein gravity coupled to a free and complex scalar field, and extend chains of mini-boson stars to the rotating case. These solutions manifest as multiple rotating mini-boson stars uniformly arranged along the rotation axis. Through numerical methods, we obtain chains of rotating mini-boson stars with one to five constituents. We show the distribution of the field functions for these chain solutions. Additionally, we also study the effect of the frequency of the complex scalar field on the ADM mass $M$ and angular momentum $J$. By comparing the conclusions of the rotating case with the non-rotating case, there are some intriguing differences. Furthermore, we observe that there exist two ergospheres for some of these solutions., Comment: 17 pages, 8 figures

In this paper, we construct the rotating multistate Proca stars (RMPSs) composed of two coexisting Proca fields including the ground state and first excited state. We consider the solution families of RMPSs in synchronized frequency and non-synchronized frequency scenarios, respectively. We discuss the characteristics of the matter fields changing with the synchronized frequency or non-synchronized frequency, and then we explore the relationship between the ADM mass $M$ and the frequency. We also analyze the characteristics of ADM mass $M$ as a function of the angular momentum $J$ simultaneously. Furthermore, we calculate the binding energy of RMPSs and analyze the stability of the solutions. Finally, we discuss the ergosphere of RMPSs., Comment: 18 pages, 9 figures

In this paper, we study solutions of a static spherically symmetric system, which is composed of the coupling with the Bardeen action and two Dirac fields. For the case where only the Bardeen action is present, the magnetic charge $q$ can be infinite, then when the magnetic charge is greater than a certain value $q_b$, there exists a black hole solution, which is called the Bardeen black hole (BBH). However, if the Dirac field is introduced, we find that the magnetic charge can only be smaller than the critical value $q_b$, in which there is no black hole solution. Moreover, in the region $q

Recently, the model of the Einstein-Bardeen theory minimally coupled to a complex, massive, free scalar field was investigated in arXiv:2305.19057. The introduction of a scalar field disrupts the formation of an event horizon, leaving only a type of solution referred to as a Bardeen-boson star. When the magnetic charge $q$ exceeds a certain critical value, the frozen Bardeen-boson star can be obtained with $\omega \rightarrow 0$. In this paper, we extend to the investigation of Einstein-Hayward-scalar model, and obtain the solution of frozen Hayward-boson star, including the ground and excited states. Furthermore, under the same parameters, it is interesting to observe that both the ground state and the excited states frozen stars have the same critical horizon and mass., Comment: 11 pages, 3 figures

We develop a symmetric traversable wormhole model, integrating Einstein's gravitational coupling phantom field and a nonlinear electromagnetic field. This work indicates the emergence of negative ADM mass within a specific parameter range, coinciding with distinct alterations in the wormhole's spacetime properties. Despite violating the Null Energy Condition (NEC) and other energy conditions, the solution exhibits unique characteristics in certain energy-momentum tensor components, potentially accounting for the manifestation of negative mass., Comment: 5 pages, 4 figures

We investigate the tidal deformability of spherically symmetric axion stars on the stable branches, including the Newtonian and relativistic branches. The results suggest that on the stable branch, the electric Love numbers of axion star are positive, while the magnetic Love numbers are negative. On the Newtonian stable branch, the electric tidal Love numbers are much larger than the magnetic ones, while on the relativistic stable branch, they are slightly larger. Furthermore, the relativistic stable branch has much smaller tidal Love numbers than the Newtonian stable branch, indicating weaker deformability of axion stars on the relativistic stable branch. This could be attributed to the fact that on the relativistic branch, axion stars are more compact, resulting hardly distorted by tidal forces., Comment: 22 pages, 5 figures

We study the accretion of relativistic Vlasov gas onto a Kerr black hole, regarding the particles as distributed throughout all the space, other than just in the equatorial plane. We solve the relativistic Liouville equation in the full $3+1$ dimensional framework of Kerr geometry. For the flow that is stationary and axial symmetric, we prove that the distribution function is independent of the conjugate coordinates. For an explicit distribution that can approximate to Maxwell-J\"{u}ttner distribution, we further calculate the particle current density, the stress energy momentum tensor and the unit accretion rates of mass, energy and angular momentum. The analytic results at large distance are shown to be consistent with the limits of the numerical ones computed at finite distance. Especially, we show that the unit mass accretion rate agrees with the Schwarzschild result in the case of low temperature limit. Furthermore, we find from the numerical results that the three unit accretion rates vary with the angle in Kerr metric and the accretion of Vlasov gas would slow down the Kerr black hole. The closer to the equator, the faster it slows down the black hole., Comment: 28 pages, 11 figures, accepted for publication in Physical Review D

In this paper, we construct a Dirac star model composed of $|\kappa|$ pairs of spinor fields. The azimuthal harmonic indeces $m$ of these spinor fields are half-integers, and they satisfiy $-(|\kappa|-\frac{1}{2})\leq m \leq |\kappa|-\frac{1}{2}$. When $\kappa=1$, it corresponds to the conventional Dirac star model, formed by two spinor fields with $m=\frac{1}{2}$ and $m=-\frac{1}{2}$. When $|\kappa|>1$, among these $|\kappa|$ pairs of spinor fields, there exist spinor fields with azimuthal harmonic indices $m>\frac{1}{2}$, and all spinor fields still conform to the same Dirac field equation. Different families of solutions are distinguished by the value of $\kappa$, so we named these solutions $\kappa$-Dirac stars. We obtain solutions for $\kappa=\pm1,\pm2,\pm3,\pm4,\pm5,\pm6$ by using numerical methods. Additionally, we compute their ADM mass $M$, Noether charge $Q$, and binding energy $E$, and illustrate how these quantities change with the spinor field's frequency $\omega$ for different $\kappa$. We observe significant differences between solutions for $|\kappa|>1$ and the $|\kappa|=1$ case. Furthermore, we provide the energy density distribution of the Dirac stars, wherein for $|\kappa|>1$ scenarios, the Dirac stars exhibit a spherical shell-like structure. Moreover, we employ three-dimensional diagrams to intuitively depict how $\kappa$ influences the combination of spinor fields to form a spherically symmetric configuration., Comment: 19 pages, 5 figures. The case of negative value $\kappa$ added, and some discussion expanded

Boson stars are potential sources of gravitational radiation. To improve our comprehension of these exotic objects, we present the study of geodesics within the space-times of stable, collapsing, and migrating boson stars. We focus on timelike geodesics that are initially circular or reciprocating. We verify that orbits initially bound within a stable boson stars persist in their bound states. For a collapsing boson star, we show that orbits initially bound and reciprocating finally either become unbound or plunge into the newly formed black hole, depending on their initial maximal radii. For initially circular geodesics, orbits with small radii plunge into the black hole; orbits with intermediate radii become unbound; and large radii orbits linger around the black hole with nonvanishing eccentricities. For the migrating case, a black hole does not form. In this case, the reciprocating orbits span a wider radial range. For initially circular geodesics, orbits with small radii become unbound, and orbits with large radii remain bound with nonvanishing eccentricities. This geodesic study provides a novel approach to investigate the gravitational collapse and migration of boson stars., Comment: 6 pages, 5 figures, comments are welcome

In this paper, we investigate the properties of the first excited state Dirac stars (DSs) with higher azimuthal harmonic index (specifically, the azimuthal harmonic indexes $m_D$ = $3/2$, $5/2$, $7/2$), as well as the relationship between the ADM mass and angular momentum of Dirac stars with respect to frequency. Moreover, We find that the ergospheres of DSs appear at lower spinor field frequencies, and both the ergospheres and the distribution of the spinor field functions are asymmetric about the equatorial plane. Furthermore, we introduce the ground state scalar field and examine its impact on this system, which is known as the multi-state Dirac-boson stars (DBSs) model. We show various types of solution families for DBSs under both synchronized frequency $\omega$ and nonsynchronized frequencies and find that similar to DSs, the spinor field and the ergospheres of DBSs are also asymmetric about the equatorial plane, but the ergospheres appear at higher spinor field frequencies., Comment: 22 pages, 8 figures

In this paper, we study the spherically symmetric Dirac star model in the presence of a phantom field, obtaining a traversable wormhole solution in non-trivial topological spacetime. This solution exhibits asymmetry in both the field configuration and the metric and possesses a finite ADM mass $M$ and Noether charge $Q$. Furthermore, we find that due to the presence of a wormhole at the center, this solution exhibits many differences from the Dirac star under trivial spacetime. Notably, when the wormhole throat size is small, our numerical calculations indicate the emergence of an extremely approximate black hole solution on one side of the wormhole spacetime, a phenomenon unexplored. At this time, the Kretschmann scalar near the throat tends to infinity, indicating the wormhole becomes untraversable., Comment: 32 pages, 23 figures

We consider a model consists of the Einstein gravity in four-dimensional spacetime, a Proca field and two Dirac fields through minimum coupling. By numerically solving this model, we obtain two types of solutions: synchronized frequency solutions and non-synchronized frequency solutions. We find that in the case of two kinds of matter fields, different families of solutions can be obtained in both synchronized and non-synchronized frequency cases, and the two families can shift to each other when certain parameters are changed. Moreover, we calculate the binding energy of multi-field solutions and give the relationship between binding energy $E$ and synchronized frequency $\tilde{\omega}$ (non-synchronized frequency $\tilde{\omega}_P$), so as to analyze the stability of the corresponding family., Comment: 22 pages, 9 figures

We consider excited configuration and multistate configuration of rotating axion boson stars~(RABSs).RABSs are asymptotically flat, stationary, spinning, horizonless solutions of Einstein-Klein-Gordon theory in which the scalar potential depends on scalar field mass $\mu$ and axion decay constant $f_a$. The excited RABSs have two types of solutions, including $^2S$ state and $^2P$ state. The rotating multistate axion boson stars~(RMABSs) consist of coupled fundamental configuration and excited configuration, and also include two types of solutions: $^1S^2S$ state and $^1S^2P$ state. Some differences between RABSs models and rotating mini-boson stars models are discussed. We show the solution space of these models for different values of decay constant $f_a$. We found fundamental RABSs have a higher maximum mass than the excited state in the low decay constant region. Moreover, the multistate configuration allows a higher mass than both the fundamental configuration and the excited configuration at the same frequency. We also found the RMABSs have the second branch in which the ergo-region emerges. This means the second branch may be superradiant unstable., Comment: 18 pages, 9 figures

In this paper, we construct the multi-state Dirac stars (MSDSs) consisting of two pairs of Dirac fields. The two pairs of Dirac fields are in the ground state and the first excited state, respectively. Each pair consists of two fields with opposite spins, ensuring spherical symmetry of the system. We discuss the solutions of the MSDSs under synchronized and nonsynchronized frequencies. By varying the mass $\tilde{\mu}_1$ of the excited state Dirac field and the frequency $\tilde{\omega}_0$ of the ground state Dirac field, we obtain different types of solutions, including single-branch and double-branch solutions. These two types of solutions do not smoothly transition into each other as the parameters $\tilde{\mu}_1$ and $\tilde{\omega}_0$ continuously change, but undergo a sudden transition when $\tilde{\mu}_1$ ($\tilde{\omega}_0$) is greater than or less than the threshold value of $0.7694$ ($0.733$). Furthermore, we analyze the characteristics of the various MSDSs solutions and analyze the relationship between the ADM mass $M$ of the MSDSs and the synchronized and nonsynchronized frequencies. Subsequently, we calculate the binding energy $E_B$ of the MSDSs and discuss the stability of the solutions. Finally, we discuss the feasibility of simulating the dark matter halos using MSDSs., Comment: 26 pages, 11 figures

In this paper, we reconsider the mixed system of BSs with wormholes at their center which performed by complex scalar field and phantom field and study a whole new condition about the potential. Both the symmetric and asymmetric solutions in the two asymptotically flat regions are obtained by using numerical method and we mainly explore the change of the results by varying the parameters of throats and potential. In ground state, we find there are multiple solutions at certain setting of parameters and with the increase of $\eta_0$ or decrease of $c$, the results gradually become single-valued functions and these two variables have similar influence to the curve shape of mass $M$ and charge $Q$, furthermore, the asymmetric solutions can turn into the solutions of symmetry at some frequency $\omega$ in certain $\eta_0$ and $c$. However, when it comes to excited state, the properties of solutions of symmetry is similar to the ground state while asymmetrical results exhibit altered characteristics. We also present the geometries of wormhole to investigate the property of this model., Comment: 23 pages, 17 figures