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In this work, we study the entropies of photons, dust (baryonic matter), dark matter, and dark energy in the context of cosmology. When these components expand freely with the universe, we calculate the entropy and specific entropy of each component from the perspective of statistics. Under specific assumptions and conditions, the entropies of these components can satisfy the second law of thermodynamics independently. Our calculations show that the specific entropy of matter cannot be a constant during the expansion of the universe except for photons. When these components interact with the space-time background, there could exist the phenomenon of particle production (annihilation). We study the influence of the interaction on the entropies of these components, and obtain the conditions guaranteeing that the entropy of each component satisfies the second law of thermodynamics., Comment: 25pages, 3figures

In this work, we investigate the quasinormal modes of a thick brane system. Considering the transverse-traceless tensor perturbation of the brane metric, we obtain the Schr\"odinger-like equation of the Kaluza-Klein modes of the tensor perturbation. Then we use the Wentzel-Kramers-Brillouin approximation and the asymptotic iteration method to solve this Schr\"odinger-like equation. We also study the numeric evolution of an initial wave packet against the thick brane. The results show that there is a set of discrete quasinormal modes in the thick brane model. These quasinormal modes appear as the decaying massive gravitons for a brane observer. They are characteristic modes of the thick brane and can reflect the structure of the thick brane., Comment: 10 pages, 6 figures, improved version

Let $\Theta$ be the Wigner time reversal operator for spin half and let $\phi$ be a Weyl spinor. Then, for a left-transforming $\phi$, the construct $\zeta_\lambda \Theta \phi^\ast$ yields a right-transforming spinor. If instead, $\phi$ is a right-transforming spinor, then the construct $\zeta _\rho \Theta \phi^\ast$ results in a left-transforming spinor ($\zeta_{\lambda,\rho}$ are phase factors). This allows us to introduce two sets of four-component spinors. Setting $\zeta_\lambda$ and $\zeta_\rho$ to $\pm i$ render all eight spinors as eigenspinor of the charge conjugation operator~$\mathcal{C}$ (called ELKO). This allows us to introduce two quantum fields. A calculation of the vacuum expectation value of the time-ordered product of the fields and their adjoints reveals the mass dimension of the fields to be one. Both fields are local in the canonical sense of quantum field theory. Interestingly, one of the fields is fermionic and the other bosonic. The mass dimension of the introduced fermionic fields and the matter fields of the Standard Model carry an intrinsic mismatch. As such, they provide natural darkness for the new fields with respect to the Standard Model doublets. The statistics and locality are controlled by a set of phases. These are explicitly given. Then we observe that in $p_\mu p^\mu = m^2$, Dirac took the simplest square root of the $4\times 4$ identity matrix $I$ (in $I \times m^2 $, while introducing $\gamma_\mu p^\mu$ as the square root of the left hand side of the dispersion relation), and as such he implicitly ignored the remaining fifteen. When we examine the remaining roots, we obtain additional bosonic and fermionic dark matter candidates of spin half. We point out that by early nineteen seventies, Dirac had suspected the existence of spin half bosons, in the same space as his fermions. Abstract truncated., Comment: 53 pages

Seeking singularity free solutions are important for further understanding black holes in quantum level. Recently, a five-dimensional singularity free black hole/topological star was constructed [Phys. Rev. Lett. 126, 151101 (2021)]. Through the Kaluza-Klein reduction, an effective four-dimensional static spherically symmetric charged black hole with scalar hair can be obtained. In this paper, we study shadow of this charged black hole with scalar hair in terms of four kinds of observers, i.e., static observers, surrounding observers, freely falling observers, and escaping observers in four-dimensional spacetime. For a spherically symmetric black hole, the shadow is circular for any observer, but the shadow size depends on the motion status of the observer. On the other hand, the effect of plasma is also investigated by a simple model. The radius of the photon sphere depends on the plasma model. Most importantly, we find that the shadow sizes do not monotonically decrease with $r$ in some cases., Comment: 12 pages, 3 figures, 2 tables

In this paper, we study the dynamics of scalar hair around a Schwarzchild black hole. The scalar hair is sourced by the Gauss-Bonnet invariant with a linear coupling. We work perturbatively in the coupling constant and ignore the back-reaction of the scalar hair and the Gauss-Bonnet invariant. We evolve the scalar field in the background of a Schwarzchild black hole and study the dynamical formation of scalar hair with different self-interactions. We integrate the energy and compute the energy flux of the scalar hair in terms of the canonical energy-momentum tensor and give the corresponding dependence on the self-interactions. Our results allow us to estimate the radiation and the condensation of scalar field with different self-interactions, these would improve our understanding for the dynamical scalarization of black holes and the possible configuration of the scalar hair in scalar Gauss-Bonnet gravity., Comment: 11 pages, 7 figures

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the cut-off parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the cut-off parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow gets more deformed with the increase of the cut-off parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the cut-off parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase of the cut-off parameter. Besides, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the cut-off parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the cut-off parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations., Comment: 16 pages, 11 figures

In this work, we investigate numerical evolution of massive Kaluza-Klein (KK) modes of a scalar field in a thick brane. We derive the Klein-Gordon equation in five dimensional spacetime, and obtain the evolution equation and the Schr\"odinger-like equation. With the resonances of the scalar KK modes as the initial data, the scalar field is evolved with the maximally dissipative boundary condition. The results show that there are scalar KK resonant particles with long life on the brane, which indicates that these resonances might be viewed as one of the candidates for dark matter., Comment: 10 pages, 5 figures. improved version

In this paper, our universe is regarded as a codimension-2 brane embedded in a noncompact six-dimensional Anti-de Sitter (AdS) spacetime. We derive the gravitational horizon radius on the brane under the low-energy approximation, which reflects how the extra dimensions cause the shortcut effect of gravitational waves (GWs). We also study the time delay between a GW signal and an electromagnetic (EM) wave signal in the low-redshift limit by combining with the joint observations of GW170817/GRB 170817A, which gives an upper limit to the $\text{AdS}_{6}^{~}$ radius as $\ell^{2}_{~} \lesssim 3.84\,\text{Mpc}^{2}_{~}$. For a high-redshift source, the time delay is converted into the discrepancy between the source redshift derived from the GW signal and the one derived from the EM counterpart. It is found that if one expects to detect the EM counterpart of a high-redshift GW event within a reasonable observation time, it requires a stronger constraint on the $\text{AdS}_{6}^{~}$ radius. Our research shows that the $\text{AdS}_{6}^{~}$ radius should satisfy $\ell^{2}_{~}\lesssim0.02\,\text{Mpc}^{2}_{~}$ for the DECIGO and BBO., Comment: 18 pages, 4 figures

Recent study shows that the magnetic reconnection can serve as an efficient mechanism to extract energy from rapidly spinning black holes. In this paper, we consider the effects of the tidal charge on the energy extraction via the magnetic reconnection in the backgrounds of a spinning braneworld black hole. With the increase of the tidal charge, we find that both the energies of the accelerated plasma and decelerated plasma decrease for the observer located at infinity. To achieve the purpose extracting the net energy from the black hole, the decelerated plasma should take negative energy. Then we observe that the power of the energy extraction via the magnetic reconnection grows with the tidal charge. Meanwhile, the efficiency also increases with the tidal charge indicating that the spinning braneworld black hole with positive tidal charge is more efficient than the Kerr black hole. Compared with the Blandford-Znajek mechanism, the magnetic reconnection process shall have a higher power for positive tidal charge. These results indicate that the tidal charge has a significant effect on the energy extraction via the magnetic reconnection process., Comment: 15 pages and 9 figures

Einstein-Gauss-Bonnet gravity in high dimensional spacetime is intriguing. Here, the properties of thick branes generated by a bulk scalar field in the five-dimensional Einstein-Gauss-Bonnet gravity were studied. With the help of the superpotential method, we obtain a series of multi-kink brane solutions. We also analyze the linear stability of the brane system under tensor perturbations and prove that they are stable. The massless graviton is shown to be localized near the brane and hence the four-dimensional Newtonian potential can be recovered. By comparing the properties of these thick branes under different superpotentials we find with some specific choice of superpotential the Gauss-Bonnet term can determine the scalar field are multi-kink or single kink., Comment: 17 pages, 18 figures

The destruction of the event horizon of a nonsingular black hole, which is not prevented by the weak cosmic censorship conjecture, might provide us the possibility to access quantum regime of gravity inside black hole. We investigate the possibility of overspinning a nonsingular rotating quantum-corrected black hole by a test particle and a scalar field in this paper, and analyse the effect of the quantum parameter on the destruction of the event horizon. For the test particle injection, both extremal and near-extremal black holes cannot be overspun due to the existence of the quantum parameter. And the larger the quantum parameter the harder the black hole to be overspun. It seems that the quantum parameter acts as a protector to prevent the black hole to be destroyed. However, for the test scalar field scattering, both extremal and near-extremal black holes can be destroyed. Due to the loop quantum gravity correction, the angular velocity of the extremal black hole shifts from that of the extremal Kerr black hole. This provides a small range of wave modes to destroy the event horizon of the quantum-corrected black hole., Comment: 19 pages, 1 figure, published version

In this paper, we study the circular orbit of the spinning test particle in the background of a rotating boson star. Using the pole-dipole approximation and neglecting the back-reaction of the spinning test particle on the spacetime, the equation of motion of the spinning test particle is described by the Mathisson-Papapetrou-Dixon equation. We solve this equation under the Tulczyjew spin-supplementary condition and obtain the four-momentum and four-velocity of the spinning test particle. Quite different from the spinless particle, the effective potential of the spinning particle with zero orbital angular momentum goes to infinite at the center of the rotating boson star. This will lead to the fact that the spinning particle can not pass through the center of the boson star. However, when the spin angular momentum and orbital angular momentum satisfy $2\bar{s}+\bar{l}=0$, the effective potential is not divergent anymore and the spinning particle can pass through the center of the rotating boson star. {We still investigate how the spin affects the structure of the circular orbits and we find that the spin will induce the larger or smaller regions of no circular orbits, unstable circular orbits, and stable circular orbits.} Moreover, the radius and energy of the circular orbit will be decreased or increased by the particle spin. These results will have an important application in testing the gravitational waves in the boson star background., Comment: 11 pages, 6 figures

A critical point is an important structure in the phase diagram of a thermodynamic system. In this work, we introduce topology to the study of the black hole thermodynamics for the first time by following Duan's topological current $\phi$-mapping theory. Each critical point is endowed with a topological charge. We find that critical points can be divided into two classes, the conventional and the novel. Further study shows that the first-order phase transition can extend from the conventional critical point, while the presence of the novel critical point cannot serve as an indicator of the presence of the first-order phase transition near it. Moreover, the charged anti-de Sitter black hole and the Born-Infeld anti-de Sitter black hole have different topological charges, which indicates they are in different topological classes from the viewpoint of thermodynamics. These give the first promising study on the topology of the black hole thermodynamics. Such approach is also expected to be extended to other black holes, and much more topological information remains to be disclosed., Comment: 6 pages and 6 figures

In this paper, the polarization modes of gravitational waves in Horndeski gravity are studied under the Palatini formalism. After obtaining the linearized equation of perturbations in Minkowski background, we find that the polarization modes of gravitational waves depend on the selection of the theoretical parameters. The polarization modes can be divided into quite rich cases by parameters. In all cases of parameter selection, there are $+$ and $\times$ modes propagating at the speed of light but no vector modes. The only difference from general relativity is scalar modes, especially the scalar degrees of freedom can be 0, 1 or 2 in different cases. The appropriate parameter cases can be expected to be selected in the detection of gravitational wave polarization modes by Lisa, Taiji and TianQin in the future., Comment: 23 pages, 1 figure, 1 table

We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Focusing on the chaotic behaviors under the perturbation, we analytically derive the Lyapunov exponent and scrambling time of the inverted harmonic oscillators. We show that the circuit complexity and Loschmidt echo exhibit qualitatively similar behaviors, particularly the consistent Lyapunov exponent., Comment: 20 pages, 2 figures, references added

Future space-borne gravitational-wave detectors will observe the gravitational waves in the milli-Hz. Extreme-mass-ratio inspirals with central supermassive black holes are very important sources that could provide the information of the vicinity of black holes. The event horizon separates the inner region of a black hole and there is nothing that can escape from this region. When the central supermassive compact object is a regular and horizonless rotating boson star, a small body could pass through the center and follow novel types of orbits. These will generate the gravitational waves that can not be obtained in the scenario corresponding to an extreme-mass-ratio inspiral with a central supermassive black hole. This can be used to examine whether a supermassive rotating boson star is present at the centers of galaxies. In this work, we consider an extreme-mass-ratio inspiral system described by a small compact object inspiralling into a central supermassive rotating boson star. Integrating four types of special equatorial geodesics and using the numerical kludge method with quadrupole approximation, we obtain the corresponding gravitational waveforms and find that there are high-frequency gravitational radiation pulses in such system. The frequencies of the gravitational radiation pulses could be in the magnitude of $10^{-1}$Hz and the whole gravitational wave parts are in the milli-Hz. By assuming the masses of the central supermassive rotating boson star and small compact object to be $10^6 M_\odot$ and $10 M_\odot$ and assuming a distance of $1\text{Gpc}$, we show that the gravitational radiation pulses could be detected by the space-borne gravitational-wave detectors. Our results will provide a possible evidence to distinguish the astrophysical compact objects in the galactic centers.

Ruppeiner geometry has been found to be a novel promising approach to uncover the microstructure of fluid systems and black holes. In this work, combining with the micro model of the Van der Waals fluid, we shall propose a first microscopic interpretation for the empirical observation of Ruppeiner geometry. Then employing the microscopic interpretation, we disclose the potential microstructure for the anti-de Sitter black hole systems. Of particular interest, we obtain the microscopic interaction potentials for the underlying black hole molecules. This significantly strengthens the study towards to the black hole nature from the viewpoint of the thermodynamics., Comment: 5 pages and 3 figures. Typos are corrected

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small-large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small-large black hole phase transition. For the six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure-temperature and temperature-horizon radius diagrams. Quite different from the liquid-vapor phase transition, a double peak behavior is present in the temperature-horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss-Bonnet gravity., Comment: 17 pages, 11 figures, and 1 table

Motion of a test particle plays an important role in understanding the properties of a spacetime. As a new type of the strong gravity system, boson stars could mimic black holes located at the center of galaxies. Studying the motion of a test particle in the spacetime of a rotating boson star will provide the astrophysical observable effects if a boson star is located at the center of a galaxy. In this paper, we investigate the timelike geodesic of a test particle in the background of a rotating boson star with angular number $m=(1, 2, 3)$. With the change of angular number and frequency, a rotating boson star will transform from the low rotating state to the highly relativistic rapidly rotating state, the corresponding Lense-Thirring effects will be more and more significant and it should be studied in detail. By solving the four-velocity of a test particle and integrating the geodesics, we investigate the bound orbits with a zero and nonzero angular momentum. We find that a test particle can stay more longer time in the central region of a boson star when the boson star becomes from low rotating state to highly relativistic rotating state. Comparing the periapse values of the orbits obtained in rotating boson stars and the corresponding orbits of the observed stars orbiting Sagittarius $A^*$, we discuss the possible observable effects of the astrophysical boson star in the Galactic center., Comment: 17 pages, 16 figures

Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical observation of the corresponding scalar curvature, we find that, for the near-extremal Kerr-AdS black hole, the repulsive interaction dominates among its microstructure. While for far-from-extremal Kerr-AdS black hole, the attractive interaction dominates. The critical phenomenon is also observed for the scalar curvature. These results uncover the characteristic microstructure of the Kerr-AdS black hole. Such general thermodynamic geometry approach is worth generalizing to other rotating AdS black holes, and more interesting microstructure is expected to be discovered., Comment: 13 pages and 6 figures

Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the black hole horizon can act as the order parameter to characterize the black hole phase transition. We also disclose that different from the five-dimensional neutral black holes, the charged ones allow the repulsive interaction among its microstructure for small black hole of higher temperature. Another significant difference between them is that the microscopic interaction changes during the small-large black hole phase transition for the charged case, where the black hole microstructure undergoes a sudden change. These results are helpful for peeking into the microstructure of charged black holes in the Gauss-Bonnet gravity., Comment: 18 pages, 15 figures, and 3 tables

By treating the order parameter as a stochastic thermal fluctuating variable for small-large black hole phase transition, we investigate the kinetic process of phase transition for the Kerr-AdS (anti-de Sitter) black holes on free energy landscape. We find that the extremal points of the off shell Gibbs free energy correspond to physical black holes. For small-large black hole phase transition, the off shell Gibbs free energy exhibits a double well behavior with the same depth. Contrary to previous research for the kinetics of phase transition for the Kerr-Newman-AdS family black holes on a free energy landscape, we find that there is a lower bound for the order parameter and the lower bound corresponds to extremal black holes. In particular, the off shell Gibbs free energy is zero instead of divergent as previous work suggested for vanishing black hole horizon radius, which corresponds to the Gibbs free energy of a thermal AdS space. The investigation for the evolution of the probability distribution for the phase transition indicates that the initial stable small (large) black hole tends to switch to stable large (small) black hole. Increasing the temperature along the coexistence curve, the switching process becomes faster and the probability distribution reaches the final stationary Boltzmann distribution at a shorter time. The distribution of the first passage time indicates the time scale of the small-large black hole phase transition, and the peak of the distribution becomes sharper and shifts to the left with the increase of temperature along the coexistence curve. This suggests that a considerable first passage process occurs at a shorter time for higher temperature. The investigation of the kinetics of phase transition might provide us new insight into the underlying microscopic interactions., Comment: 16 pages, 10 figures, published version

The space-based gravitational wave (GW) detector LISA is expected to observe signals from a large population of compact object binaries, comprised predominantly of white dwarfs, in the Milky Way. Resolving individual sources from this population against its self-generated confusion noise poses a major data analysis problem. We present an iterative source estimation and subtraction method to address this problem based on the use of particle swarm optimization (PSO). In addition to PSO, a novel feature of the method is the cross-validation of sources estimated from the same data using different signal parameter search ranges. This is found to greatly reduce contamination by spurious sources and may prove to be a useful addition to any multi-source resolution method. Applied to a recent mock data challenge, the method is able to find $O(10^4)$ Galactic binaries across a signal frequency range of $[0.1,15]$ mHz, and, for frequency $\gtrsim 4$ mHz, reduces the residual data after subtracting out estimated signals to the instrumental noise level., Comment: 17 pages, 11 figures; Accepted in Phys. Rev. D; Correct spellings of author names

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this letter, we carry out the first investigation of dynamical phase behaviour at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we find that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behaviour in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions., Comment: 6 pages and 6 figures

Nonlinear electrodynamic (NLED) theories are well-motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in seeking for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED models: the Euler-Heisenberg NLED model and the Bronnikov NLED model, and calculate the weak deflection angle of light by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynamics on the deflection angle and analyse the behavior of the deflection angle by a regular magnetically charged black hole. It is found that the weak deflection angle of the electrically charged Einstein-Euler-Heisenberg black hole increases with the one-loop corrections and the regular magnetically charged black hole based on the Bronnikov NLED model has a smaller deflection angle than the singular one. Besides, we also calculate the deflection angle of light by the geodesic method for verification. In addition, we discuss the effects of a cold non-magnetized plasma on the deflection angle and find that the deflection angle increases with the plasma parameter.

In this paper, we study the structure and gravitational resonances of thick branes generated by a mimetic scalar field in $f(R)$ gravity. We obtain several typical thick brane solutions for $f(R)=R+\alpha R^2$. To study their stability, we analyze the tensor perturbation of the metric. It is shown that any thick brane model with $df/dR>0$ is stable and the graviton zero mode can be localized on the brane for each solution, which indicates that the four-dimensional Newtonian gravity can be restored. The effect of the parameter $\alpha$ on the gravitational resonances is studied. As a brane splits into multi sub-branes, the effective potential of the tensor perturbation will have an abundant inner structure with multi-wells, and this will lead to new phenomena of the gravitational resonances., Comment: 16 pages, 26 figures

In this paper, we investigate a $6$-dimensional smooth thick braneworld model which contains a compact extra dimension and an infinite large one. The braneworld is generated by a real scalar field with a $\phi^6$ potential and the bulk is asymptotically $\text{AdS}_6$ spacetime. The geometry achieves the localization of the free $U(1)$ gauge field, which is a problem in the $5$-dimensional Randall-Sundrum-like models. In addition, we analyze the stability of the braneworld system and the localization of gravitons., Comment: 15 pages, 11 figures

The destruction of a regular black hole event horizon might provide us the possibility to access regions inside black hole event horizon. This paper investigates the possibility of overcharging a charged Taub-NUT regular black hole via the scattering of a charged field and the absorption of a charged particle. For the charged scalar field scattering, both the near-extremal and extremal charged Taub-NUT regular black holes cannot be overcharged. For the test charged particle absorption, the result shows that the event horizon of the extremal charged Taub-NUT regular black hole still exists while the event horizon of the near-extremal one can be destroyed. However, if the charge and energy cross the event horizon in a continuous path, the near-extremal charged Taub-NUT regular black hole might not be overcharged., Comment: 22 pages, 3 figures

In this paper, we study the Hawking temperature of the BTZ black hole based on the purely topological method proposed by Robson, Villari, and Biancalana (RVB) [Phys. Rev. D 99, 044042 (2019)]. The Hawking temperature of the charged rotating BTZ black hole can be accurately derived by this topological method. We also calculate the Hawking temperature of the BTZ black hole in massive gravity. Because the metric function of the BTZ black hole in massive gravity has a mass term, the corresponding Hawking temperature cannot be derived unless an integral constant is added., Comment: 6 pages, 1 figure, accepted by Physics Letters B

Considering a thermal state of the dual CFT with a uniform deformation by a scalar operator, we study a holographic renormalization group flow at nonzero temperature in the bulk described by the Einstein-scalar field theory with the self-interaction term $\lambda \phi^4$ in asymptotic anti-de Sitter spacetime. We show that the holographic flow with the self-interaction term could run smoothly through the event horizon of a black hole and deform the Schwarzschild singularity to a Kasner universe at late times. Furthermore, we also study the effect of the scalar self-interaction on the deformed near-singularity Kasner exponents and the relationship between entanglement velocity and Kasner singularity exponents at late times., Comment: 11 pages, 3 figures

Understanding the dynamic process of the thermodynamic phase transition can provide the deep insight into the black hole microscopic properties and structures. We in this paper study the dynamic properties of the stable small-large black hole phase transition for the five-dimensional neutral Gauss-Bonnet AdS black hole. Firstly, by using the first law of black holes, we prove that the extremal points of the free energy on the landscape denote the real black hole solutions satisfying the field equations. The local maximal and minimal points correspond to local unstable and stable black hole states, respectively. Especially, on the free energy landscape, the wells of the coexistence small and large black holes have the same depth. Then we investigate the probability evolution governed by the Fokker-Planck equation. Due to the thermal fluctuation, we find that the small (large) black hole state can transit to the large (small) black hole state. Furthermore, the first passage time is calculated. For each temperature, a single peak is presented, which suggests that there is a considerable fraction of the first passage events taking place at short time. And the higher the temperature is, the faster decrease of the probability is. These results will uncover some intriguing dynamic properties of the stable small-large black hole phase transition in modified gravity., Comment: 17 pages, 10 figures

We study brane worlds in an anisotropic higher-dimensional spacetime within the context of $f(R)$ gravity. Firstly, we demonstrate that this spacetime with a concrete metric ansatz is stable against linear tensor perturbations under certain conditions. Moreover, the Kaluza-Klein modes of the graviton are analyzed. Secondly, we investigate thick brane solutions in six dimensions and their properties. We further exhibit two sets of solutions for thick branes. At last, the effective potential of the Kaluza-Klein modes of the graviton is discussed for the two solved $f(R)$ models in higher dimensions., Comment: 30 pages, 10 figures; Sec IV updated; Appendix C added; minor other changes made; matches the published version

In this work, we investigate the gravitational resonances in various $f(T)$-brane models with the warp factor $\text{e}^{A(y)}=\tanh\big(k(y+b)\big)-\tanh\big(k(y-b)\big)$. For three kinds of $f(T)$, we give the solutions to the system. Besides, we consider the tensor perturbation of vielbein and obtain the effective potentials by the Kaluza-Klein (KK) decomposition. Then, we analyze what kind of effective potential can produce the gravitational resonances. Effects of different parameters on the gravitational resonances are analysed. The lifetimes of the resonances could be long enough as the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates of dark matter. Combining the current experimental observations, we constrain the parameters for these brane models., Comment: 12 pages, 14 figures

In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant $-\frac{1}{8}$. In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity., Comment: 16 pages and 8 figures

It has been shown that the nonthermal spectrum of Hawking radiation will lead to information-carrying correlations between emitted particles in the radiation. The mutual information carried by such correlations can not be locally observed and hence is dark. With dark information, the black hole information is conserved. In this paper, we look for the spherically symmetric black hole solution in a $\lambda\varphi$ fluid model and investigate the radiation spectrum and dark information of the black hole. The spacetime structure of this black hole is similar to that of the Schwarzschild one, while its horizon radius is decreased by the $\lambda\varphi$ fluid. By using the statistical mechanical method, the nonthermal radiation spectrum is calculated. This radiation spectrum is very different from the Schwarzschild case at its last stage because of the effect of the $\lambda\varphi$ fluid. The $\lambda\varphi$ fluid reduces the lifetime of the black hole, but increases the dark information of the Hawking radiation., Comment: 12 pages, 6 figures

Universal relations and constants have important applications in understanding a physical theory. In this article, we explore this issue for Hawking-Page phase transitions in Schwarzschild anti-de Sitter black holes. We find a novel exact dual relation between the minimum temperature of the ($d$+1)-dimensional black hole and the Hawking-Page phase transition temperature in $d$ dimensions, reminiscent of the holographic principle. Furthermore, we find that the normalized Ruppeiner scalar curvature is a universal constant at the Hawking-Page transition point. Since the Ruppeiner curvature can be treated as an indicator of the intensity of the interactions amongst black hole microstructures, we conjecture that this universal constant denotes an interaction threshold, beyond which a virtual black hole becomes a real one. This new dual relation and universal constant are fundamental in understanding Hawking-Page phase transitions, and might have new important applications in the black hole physics in the near future., Comment: 5 pages and 4 figures

Recently, a novel four-dimensional Einstein-Gauss-Bonnet (EGB) theory was presented to bypass the Lovelock's theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $\alpha\rightarrow\alpha/(D-4)$ and to take the limit $D\rightarrow4$. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem [arXiv:2003.11552, arXiv:2003.12771, arXiv:2004.08362, arXiv:2004.09472, arXiv:2004.10716]. The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss-Bonnet term in four dimensions contributes to the string geometry in the new theory., Comment: 20 pages, 9 figures, published version

In this paper, thick branes generated by the mimetic scalar field with Lagrange multiplier formulation are investigated. We give three typical thick brane background solutions with different asymptotic behaviors and show that all the solutions are stable under tensor perturbations. The effective potentials of the tensor perturbations exhibit as volcano potential, Po\"{o}schl-Teller potential, and harmonic oscillator potential for the three background solutions, respectively. All the tensor zero modes (massless gravitons) of the three cases can be localized on the brane. We also calculate the corrections to the Newtonian potential. On a large scale, the corrections to the Newtonian potential can be ignored. While on a small scale, the correction from the volcano-like potential is more pronounced than the other two cases. Combining the specific corrections to the Newtonian potential of these three cases and the latest results of short-range gravity experiments, we get the constraint on the scale parameter as $k\gtrsim 10^{-4}$eV, and constraint on the corresponding five-dimensional fundamental scale as $M_\ast \gtrsim10^5$TeV., Comment: 12 pages, 5 fugures

A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by D. Glavan and C. Lin [Phys. Rev. Lett. 124, 081301 (2020)], which is intended to bypass the Lovelock's theorem and to yield a non-trivial contribution to the four-dimensional gravitational dynamics. However, the validity and consistency of this theory has been called into question recently. We study a static and spherically symmetric black hole charged by a Born-Infeld electric field in the novel four-dimensional Einstein-Gauss-Bonnet gravity. It is found that the black hole solution still suffers the singularity problem, since particles incident from infinity can reach the singularity. It is also demonstrated that the Born-Infeld charged black hole may be superior to the Maxwell charged black hole to be a charged extension of the Schwarzschild-AdS-like black hole in this new gravitational theory. Some basic thermodynamics of the black hole solution is also analyzed. Besides, we regain the black hole solution in the regularized four-dimensional Einstein-Gauss-Bonnet gravity proposed by H. L\"u and Y. Pang [arXiv:2003.11552]., Comment: 13 pages and 18 figures, published version

In this work, kink-antikink collision in a two-dimensional Lorentz-violating $\phi^4$ model is considered. It is shown that the Lorentz-violating term in the proposed model does not affect the structure of the linear perturbation spectrum of the standard $\phi^4$ model, and thus there exists only one vibrational mode. The Lorentz-violating term impacts, however, the frequency and spatial wave function of the vibrational mode. As a consequence, the well-known results on $\phi^4$ kink-antikink collision will also change. Collisions of kink-antikink pairs with different values of initial velocities and Lorentz-violating parameters are simulated using the Fourier spectral method. Our results indicate that models with larger Lorentz-violating parameters would have smaller critical velocities $v_c$ and smaller widths of bounce windows. Interesting fractal structures existing in the curves of maximal energy densities of the scalar field are also found., Comment: 8 pages, 9 figures, final version published by Phys. Lett. B

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity., Comment: 17 pages, 9 figures, and 2 tables, references added. Accepted for publication in PRD

In this paper, we investigate the motion of a classical spinning test particle orbiting around a static spherically symmetric black hole in a novel four-dimensional Einstein-Gauss-Bonnet gravity [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)]. We find that the effective potential of a spinning test particle in the background of the black hole has two minima when the Gauss-Bonnet coupling parameter $\alpha$ is nearly in a special range $-6.1<\alpha/M^2<-2$ ($M$ is the mass of the black hole), which means such particle can be in two separate orbits with the same spin angular momentum and orbital angular momentum. We also investigate the innermost stable circular orbits of the spinning test particle and find that the effect of the particle spin on the the innermost stable circular is similar to the case of the four-dimensional black hole in general relativity., Comment: 10 pages, 5 figures

The recent discovery of the novel four-dimensional static and spherically symmetric Gauss-Bonnet black hole provides a promising bed to test Gauss-Bonnet gravity by using astronomical observations [Phys. Rev. Lett. 124, 081301 (2020)]. In this paper, we first obtain the rotating Gauss-Bonnet black hole solution by using the Newman-Janis algorithm, and then study the shadow cast by the nonrotating and rotating candidate Gauss-Bonnet black holes. The result indicates that positive metric parameter $\alpha$ shrinks the shadow, while negative one enlarges it. Meanwhile, both the distortion and ratio of two diameters of the shadow are found to increase with the metric parameter for certain spin. Comparing with the Kerr black hole, the shadow gets more distorted for $\alpha$, and less distorted for negative one. Furthermore, we calculate the angular diameter of the shadow by making use of the observation of M87*. The result indicates that negative metric parameter $\alpha$ in (-4.5, 0) is more favored. Since the negative energy appears for negative $\alpha$, our results extends the study of Gauss-Bonnet gravity. We believe further study on the four-dimensional rotating black hole may shed new light on Gauss-Bonnet gravity., Comment: 19 pages, 7 figures, comments and references added, modified version

In [Phys. Rev. Lett. 124, 101103 (2020)], a universal relation between corrections to entropy and extremality was proposed. The relation was also found to exactly hold for the four-dimensional charged AdS black hole. In this paper, we extend the study to the rotating BTZ and Kerr-AdS black holes when a constant correction to General Relativity is considered for the first time. The entropy and extremality bound are calculated, and they have a closely dependent behavior with the coupling parameter of the constant correction. We confirm the universal relation for the rotating AdS black holes. Furthermore, taking into consideration of the shift of the angular momentum, we confirm one more new universal relation for the rotating cases. In particular, we state a conjecture on a universal relation, which gives a universal conjecture relation between the shifted thermodynamic quantities for arbitrary black hole background. We believe that these universal relations will shed new light on the region of the quantum gravity., Comment: 8 pages, 2 figures

Recently, black hole thermodynamics and phase transition have been studied in the extended phase space. Besides the VdW-like phase transition, more interesting phase transitions were found. More interestingly, combining with the thermodynamic geometry, the microstructure of black holes was investigated.In this paper, we give a brief review of recent progress on this subject., Comment: 4 pages, 1 figure. Invited News & Views by Science Bulletin

The recent detections of the gravitational wave (GW) event GW170817 and its electromagnetic counterpart GRB 170817A produced by a binary neutron star (NS) merger is a new milestone of multimessenger astronomy. The time interval between these two signals has attracted widespread attention from physicists. In the braneworld scenario, GWs could propagate through the bulk while electromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe. Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWs and EMWs are originated simultaneously from the same source on the brane, they are expected to arrive at the observer successively. Consequently, the time delay between GW170817 and GRB 170817A may carry the information of the extra dimension. In this paper, we try to investigate the phenomenon in the context of a five-dimensional dS ($\text{dS}_5$) spacetime. We first study two special Universe models, i.e., de Sitter and Einstein-de Sitter models, and calculate the gravitation horizon radius in each case. For the real Universe, we then consider the $\Lambda$CDM model. Our results show that for the de Sitter model of the Universe, the $\text{dS}_5$ radius could not contribute to the time delay. With the data of the observation, we constrain the $\text{dS}_5$ radius to $\ell\gtrsim7.5\times10^{2}\,\text{Tpc}$ for the Einstein-de Sitter model and $\ell\gtrsim2.4\times10^{3}\,\text{Tpc}$ for the $\Lambda$CDM model. After considering the uncertainty in the source redshift and the time-lags given by different astrophysical processes of the binary NS merger, we find that our constraints are not sensitive to the redshift in the range of (0.005, 0.01) and the time-lag in the range of (-100s, 1.734s)., Comment: 13 pages, 3 figures, published version

Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black hole can be over-spun. By comparing the two methods, the results indicate the time interval for particles crossing the black hole horizon might be important for consideration of the weak cosmic censorship conjecture., Comment: 11 pages, 1 figure