In this paper, we investigated the Dirac and Klein-Gordan equations, as well as the greybody factor for a Schwarzschild black hole (SBH) immersed in quintessence and associated with a cloud of strings. Primarily, we study the Dirac equation using a null tetrad in the Newman- Penrose (NP) formalism. Next, we separate the Dirac equation into radial and angular sets. Using the radial equations, we study the profile of effective potential by transforming the radial equation of motion into standard Schr% ödinger wave equations form through tortoise coordinate. Similarly, we study the Klein-Gordan equation in this spacetime. The Miller-Good transformation method is employed to compute the greybody factor of bosons. To compute the Gerybody factor for fermions, we use the general method of semi-analytical bounds. We also investigate the effect of string clouds and quintessence parameters on Hawking radiation. According to the results, the greybody factor is strongly influenced by the shape of the potential, which is determined by the model parameters. This is consistent with the ideas of quantum mechanics; as the potential rises, it becomes harder for the wave to penetrate.
In this paper we are discussing the problem of low-energy greybody factors for fermions emitted by a Schwarzschild-de Sitter black hole. In our study we are using the analytical methods proposed by Unruh some time ago for determining the greybody factors. We have found that at low energies the greybody factors are constant for a given total angular momentum (similar to what happens in the case of scalar particles reported before in the literature). Also our results are indicating an enhancement in the energy spectrum if one is increasing the value of the cosmological constant. These results ar…
The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin-(1/2) in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterward, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into a Schrödinger like differ…
In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a "transfer matrix" formalism), are …
In this work, we have considered a $n-$dimensional Schwarzschild-Tangherlini black hole spacetime with massless minimally coupled free scalar fields in its bulk and $3-$brane. The bulk scalar field equation is separable using the higher dimensional spherical harmonics on $(n-2)-$sphere. First, using the Hamiltonian formulation with the help of the recently introduced near-null coordinates we have obtained the expected temperature of the Hawking effect, identical for both bulk and brane localized scalar fields. Second, it is known that the spectrum of the Hawking effect as seen at asymptotic fu…
Greybody factors in black hole physics modify the naive Planckian spectrum that is predicted for Hawking radiation when working in the limit of geometrical optics. We consider the Schwarzschild geometry in (3+1) dimensions, and analyze the Regge-Wheeler equation for arbitrary particle spin S and wave-mode angular momentum L, deriving rigourous bounds on the greybody factors as a function of S, L, wave frequency (omega), and the black hole mass, m.
We investigate the shadow, deflection angle, and the greybody bounding of a Schwarzschild-AdS/dS black hole in scale-dependent gravity. We used the EHT data to constrain the parameter $ε$. We have found that within the $1σ$ level of uncertainty, $εM_0$ ranges at $10^{-11} - 10^{-16}$ orders of magnitude for Sgr. A*, and $10^{-11} - 10^{-17}$ for M87*. Using these parameters, we explored how the shadow radius behaves as perceived by a static observer. Using the known parameters for Sgr. A* and M87*, we found different shadow cast behavior near the cosmological horizon even if the same scaling p…
We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensib…
Greybody factors of Proca fields in Schwarzschild spacetime: A supplemental analysis based on decoupled master equations related to the Frolov-Krtouš-Kubizňák-Santos separation
The Institute for Fundamental Study, Naresuan University（纳瑞宣大学基础研究所）
Greybody Factors, Absorption Cross Sections and Hawking Radiation of Holonomy-Corrected Schwarzschild Black Holes
University of Hradec Králové（赫拉德茨克拉洛韦大学）；Kimyo International University in Tashkent（塔什干金学院国际大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；Ulugh Beg Astronomical Institute（乌鲁伯格天文研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
In this paper, we have examined the geodesic structure of the spacetime surrounding Schwarzschild black holes in the presence of a quintessence field parameter $q$ and string cloud parameter $a$. Because of the quintessence field, there are two horizon structures and coordinate time $t$ shows some fascinating variations due to the parameters. We do a thorough investigation of the existence of critical orbits for various parameter values.
In this paper, we study the scattering and absorption sections of the Schwarzschild--anti de Sitter black hole surrounded by quintessence. The critical values of the cosmological constant and the normalization factor are obtained. We describe the event horizons and the extremal condition of the black hole surrounded by quintessence. The effects of quintessence on the classical and semi--classical scattering cross--sections have been estimated. Also, the absorption section is studied with the sinc approximation in the eikonal limit. We consider the quintessence state parameter in the particular…
In this manuscript, we consider a deformation on the Heisenberg algebra and investigate the effects on the thermodynamics of the Schwarzschild black hole that is surrounded by quintessence matter. To this end, we obtain the temperature, entropy, and heat capacity functions of the black hole by using the standard laws of thermodynamic according to the considered deformation. We show that upper and lower bound values appear on these functions based on the quintessence and deformed algebra. Then, we derive the corrected density of quintessence matter and the black hole's equation of state functio…
In Schwarzschild's acoustic black hole (SABH) spacetime, we investigate the wave dynamics for the fermions. To this end, we first take into account the Dirac equation in the SABH by employing a null tetrad in the Newman-Penrose (NP) formalism. Then, we consider the Dirac and Rarita Schwinger equations, respectively. The field equations are reduced to sets of radial and angular equations. By using the analytical solution of the angular equation set, we decouple the radial wave equations and obtain the one-dimensional Schrödinger like wave equations with their effective potentials. The obtained …
The thermodynamic and spectroscopic behaviour of Schwarzschild black hole surrounded by quintessence are studied. We have derived the thermodynamic quantities and studied their behaviour for different values of quintessence parameter. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Elucidean time. Also assuming that the adiabatic invariant obeys Bohr-Sommerfeld quantization rule, detailed study of area spectrum and entropy spectrum have been done for special cases of the quintessece state parameter. We find that the spectra are equally space…
In this paper, we evaluated the quasinormal modes of electromagnetic perturbation in a Schwarzschild black hole surrounded by the static spherically symmetric quintessence by using the third-order WKB approximation when the quintessential state parameter $ w_{q}$ in the range of $-1/3<w_{q}<0$. Due to the presence of quintessence, Maxwell field damps more slowly. And when at $-1<w_{q}<-1/3$, it is similar to the black hole solution in the ds/Ads spacetime. The appropriate boundary conditions need to be modified.
An analysis of the energy-momentum localization for a four-dimensional\break Schwarzschild black hole surrounded by quintessence is presented in order to provide expressions for the distributions of energy and momentum. The calculations are performed by using the Landau-Lifshitz and Weinberg energy-momentum complexes. It is shown that all the momenta vanish, while the expression for the energy depends on the mass $M$ of the black hole, the state parameter $w_{q}$ and the normalization factor $c$. The special case of $w_{q}=-2/3$ is also studied, and two limiting cases are examined.
In this paper we study the properties of Schwarzschild black hole surrounded by quintessence matter. The main objective of the paper is to show the existence of Nariai type black hole for special values of the parameters in the theory. The Nariai black hole with the quintessence has the topology $dS_2 \times S_2$ with $dS_2$ with a different scalar curvature than what would be expected for the Schwarzschild-de Sitter degenerate black hole. Temperature and the entropy for the Schwarzschild-de Sitter black hole and the Schwarzschild-quintessence black hole are compared. The temperature and the c…
We present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field $u$ plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass $u$ increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly and the frequencies having a limited value. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.
We evaluate the quasinormal modes of massless Dirac perturbation in a Schwarzschild black hole surrounded by the free static spherically symmetric quintessence by using the third-order WKB approximation. The result shows that due to the presence of quintessence, the massless field damps more slowly. The real part of the quasinormal modes increases and the the absolute value of the imaginary part increases when the state parameter $w_q$ increases. In other words, the massless Dirac field decays more rapidly for the larger $w_q$. And the peak value of potential barrier gets higher as $|k|$ incre…
Black hole thermodynamic stability can be determined by studying the nature of heat capacity of the system. For Schwarzschild black hole the heat capacity is negative, but in the quintessence field this system shows a second order phase transition, implying the existence of a stable phase. We further discuss the equation of state of the present system. While analyzing the quasinormal modes, we find that the massive scalar quasinormal mode frequencies in the complex $ω$ plane shows a dramatic change when we plot it as a progressive function of quintessence state parameter. We also find the Hawk…
The evolution of scalar, electromagnetic and gravitational fields around spherically symmetric black hole surrounded by quintessence are studied with special interest on the late-time behavior. In the ring down stage of evolution, we find in the evolution picture that the fields decay more slowly due to the presence of quintessence. As the quintessence parameter εdecreases, the decay of l=0 mode of scalar field gives up the power-law form of decay and relaxes to a constant residual field at asymptotically late times. The l>0 modes of scalar, electromagnetic and gravitational fields show a powe…
In this paper, we formulate an analytic expression of the greybody factor for the Kerr-Newman black hole in the presence of the quintessential field. Primarily, we analyze the profile of effective potential by transforming the radial equation of motion into standard Schr$\ddot{o}$dinger form through tortoise coordinate. The two asymptotic solutions, in the form of hypergeometric functions, are computed at distinct radial regions such as a black hole and cosmological horizons determined by the quintessence. To extend the viability over the whole radial regime, we match the analytical solutions …
The late-time evolution of Dirac field around spherically symmetric black hole surrounded by quintessece is studied numerically. Our results show, for lower values of the quintessence state parameter ε, Dirac field decays as power-law tail but with a slower decay rate than the corresponding Schwarzschild case. But for ε<-1/3, all the \ell-poles of the Dirac field give up the power-law decay form and relax to a constant residual field at asymptotically late times. The value of this residual field for which the field settles down varies on different surfaces. It has the lowest value on the black…
In this work, we consider the propagation of scalar particles in a higher-dimensional Schwarzschild-de-Sitter black-hole spacetime, both on the brane and in the bulk. Our analysis applies for arbitrary partial modes and for both minimal and non-minimal coupling of the scalar field. A general expression for the greybody factor is analytically derived in each case, and its low-energy behaviour is studied in detail. Its profile in terms of scalar properties (angular-momentum number and non-minimal coupling parameter) and spacetime properties (number of extra dimensions and cosmological constant) …
Marginally stable circular orbits (MSCOs) of a massive test particle are investigated in the spacetime geometry of Schwarzschild black hole surrounded by quintessence. For that matter we consider three important scenarios where the equation of state parameter $ω_{q}$, has one of the following forms (i) $ω_q=-1$ (ii) $ω_q=-2/3$ and (iii) $ω_q= -1/3$. The existence of such marginally stable circular orbits in these scenarios depend on the range of normalization factor $α$. Briefly, we show that in the first case such orbits exist only if $0<α<4/16875$. Moreover in the second case which is a spec…
In this paper, the quasinormal modes of gravitational perturbation around a Schwarzschild black hole surrounded by quintessence were evaluated by using the third-order WKB approximation. Due to the presence of quintessence, the gravitational wave damps more slowly.
Probing Schwarzschild-like Black Holes in Metric-Affine Bumblebee Gravity with Accretion Disk, Deflection Angle, Greybody Bounds, and Neutrino Propagation
Finding exact solutions for black-hole greybody factors is generically impractical; typically one resorts either to making semi-analytic or numerical estimates, or alternatively to deriving rigorous analytic bounds. Indeed, rigorous bounds have already been established for the greybody factors of Schwarzschild and Riessner-Nordstrom black holes, and more generally for those of arbitrary static spherically symmetric asymptotically flat black holes. Adding rotation to the problem greatly increases the level of difficulty, both for purely technical reasons (the Kerr or Kerr-Newman black holes are…
An exact solution was recently found in the massive gravity theory having the form of Schwarzschild-dS black holes with some additional background fields. Hawking radiation will occur at the event and cosmological horizons having the blackbody spectrum, which will be modified by the geometry outside the black hole. In this paper, we study the greybody factors of a test scalar, considering its minimal coupling with the background geometry. The case of small black holes with the horizon radius much smaller than the cosmological dS radius is studied numerically. The case of near-extremal black ho…
We study the Quasinormal Modes (QNMs) of the Schwarzschild black hole surrounded by a quintessence field after implementing the quantum corrections to its solution as required by the Generalised Uncertainty Principle (GUP). We analyse the dependence of the QNMs on the deformation parameters of GUP as well as on the quintessence parameter. In most cases the QNMs show the appreciable dependency on these parameters. For a better idea of the accuracy of calculations of QNMs, we compare the results of the QNMs obtained via Mashhoon method with the 6th order WKB method. A good agreement between thes…
In this manuscript, we investigate the effects of a modified dispersion relation on the thermodynamics of Schwarzschild black hole surrounded by the quintessence matter. We find that the MDR-correction states the same lower bound on the horizon, while the quintessence matter specifies the upper bound to the horizon depending on the state parameter. Due to MDR-correction and quintessence matter presence, we observe modifications in equation of state and specific heat functions of black hole. We show that a remnant can occur according to quintessence matter, and the black hole's stability depend…
We study the quasi-normal modes for scalar, electromagnetic, and gravitational axial perturbations in the Hayward regular black hole surrounded by quintessence (HBH-$ω_q$). Using the third--order WKB approximation we can determine the dependence of the quasi--normal modes on the parameters of the regular black hole and the parameters on the test fields. We also determine the greybody factor, giving transmission and reflection coefficients of the scattered wave through the effective potentials in the WKB approximation using numerical analysis.
We have studied the null geodesics of the Schwarzschild black hole surrounded by quintessence matter. Quintessence matter is a candidate for dark energy. Here, we have done a detailed analysis of the geodesics and exact solutions are presented in terms of Jacobi-elliptic integrals for all possible energy and angular momentum of the photons. The circular orbits of the photons are studied in detail. As an application of the null geodesics, the angle of deflection of the photons are computed.
We investigate the effect of quantum correction on Hawking radiation for Schwarzschild black holes. We consider Hawking temperature and entropy to order G^2 and find that the area law of black holes should be modified. We think of Hawking radiation as tunneling and find that at certain frequency ω the radiation spectrum of black holes can be pure blackbody spectrum. Therefore, it is possible to break down information conservation. In order to ensure information conservation at any energy scales, we suggest that black holes cannot release all information they have. We briefly discuss the bound …
We investigate the dynamics of a neutral and a charged particle around a static and spherically symmetric black hole in the presence of quintessence matter and external magnetic field. We explore the conditions under which the particle moving around the black hole could escape to infinity after colliding with another particle. The innermost stable circular orbit (ISCO) for the particles are studied in detail. Mainly the dependence of ISCO on dark energy and on the presence of external magnetic field in the vicinity of black hole is discussed. By using the Lyapunov exponent, we compare the stab…
Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
In this paper, we examine the weak deflection angle and greybody bound for magnetized regular black hole.$~$ For this purpose, we apply the Gauss-Bonnet theorem on the black hole and obtain the deflection angle in plasma and non-plasma mediums.$~$ Moreover, we investigate graphically the effect of impact parameter on the deflection angle for regular black hole in both mediums. We examine that deflection angle goes to infinity when the impact parameter approaches to zero. We also observe that deflection angle shows negative behaviour at $q=0.6$ and $q=2.09$ but at $0.6<q<2.09$, angle shows the …
In this paper, we study the weak deflection angle of black hole in effective loop quantum gravity using the geometrical technique used by Gibbons and Werner. We first derive the optical metric, calculate the Gaussian optical curvature, and then apply the Gauss-Bonnet theorem. We then also investigate the effect of plasma and dark matter mediums on the weak deflection angle. We show that increasing the impact of these two mediums grows the deflection angle. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we d…
We study the time-like geodesic congruences, in the space-time geometry of a Schwarzschild black hole surrounded by quintessence. The nature of effective potential along with the structure of the possible orbits for test particles in view of the different values of quintessence parameter are analysed in detail. %wherever possible it is done analytically otherwise numerically. An increase in quintessence parameter is seen to set the particles from farther distance into motion around black hole. The effect of quintessence parameter is investigated analytically wherever possible otherwise we perf…
It is well known that quantum effects may lead to remove the intrinsic singularity point of back holes. Also, the quintessence scalar field is a candidate model for describing late-time acceleration expansion. Accordingly, Kazakov and Solodukhin considered the existence of back-reaction of the spacetime due to the quantum fluctuations of the background metric to deform Schwarzschild black hole, which led to change the intrinsic singularity of the black hole to a 2-sphere with a radius of the order of the Planck length. Also, Kiselev rewrote the Schwarzschild metric by taking into account the q…
Extending a computation which appeared recently in hep-th/0301173, we compute the transmission and reflection coefficients for massless uncharged scalars and gravitational waves scattered by d>=4 Schwarzschild or d=4 Reissner-Nordstrom black holes, in the limit of large imaginary frequencies. The transmission coefficient has an interpretation as the "greybody factor" which determines the spectrum of Hawking radiation. The result has an interesting structure and we speculate that it may admit a simple dual description; curiously, for Reissner-Nordstrom the result suggests that this dual descrip…
