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 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…
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.
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, 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.
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…
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, 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 e…
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 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…
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 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…
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…
By considering the back-reaction of the spacetime through the spherically symmetric quantum fluctuations of the background metric, Kazakov and Solodukhin removed the singularity of the Schwarzschild black hole. This regular Schwarzschild black hole has a spherical central region with a radius of the order of the Planck length. On the other hand, due to the positively accelerating expansion of the Universe, it seems that there exists a universal repulsive force known as dark energy. In the framework of quantum field theories, the quintessence field is a candidate model for investigating and mod…
Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Ref. \cite{Mustafa:2021}. In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, besides taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test parti…
Present paper provides a new model of anisotropic strange star corresponding to the exterior schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori Barua (KB) ansatz in presence of quintessence field characterized by a parameter omegaq . The obtained solutions are free from central singularity. Our model is potentially stable.The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1)(radius=7.07 km),4U1820- 30 (radius=10 km),Vela X-12 (radius=9.99 km),PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observat…
Basing on the ideas used by Kiselev, we study three black holes surrounded by quintessence and the effects of quintessence on the classical and semiclassical scattering cross-sections. In contrast, the absorption section is studied with the sinc approximation in the eikonal limit. For Schwarzschild, Reissner-Nordström and Bardeen black holes surrounded by quintessence, the values critical of charges and the normalization factor are obtained. We also described the horizons and the extremal condition of the black holes surrounded by quintessence. By setting for the quintessence state parameter i…
In this paper, we concern about applying general relativistic tests on the spacetime produced by a static black hole associated with cloud of strings, in a universe filled with quintessence. The four tests we apply are precession of the perihelion in the planetary orbits, gravitational redshift, deflection of light, and the Shapiro time delay. Through this process, we constrain the spacetime's parameters in the context of the observational data, which results in about $\sim 10^{-9}$ for the cloud of strings parameter, and $\sim 10^{-20}$ m$^{-1}$ for that of quintessence. The response of the b…
In this paper, we investigate analytically the level space of the imaginary part of quasinormal frequencies for a black hole with a deficit solid angle and quintessence-like matter by the Padmanabhan's method \cite{Padmanabhan}. Padmanabhan presented a method to study analytically the imaginary part of quasinormal frequencies for a class of spherically symmetric spacetimes including Schwarzschild-de Sitter black holes which has an evenly spaced structure. The results show that the level space of scalar and gravitational quasinormal frequencies for this kind of black holes only depend on the su…
We have studied accretion of the dark matter and dark energy onto of $(n+2)$-dimensional Schwarzschild black hole and Morris-Thorne wormhole. The mass and the rate of change of mass for $(n+2)$-dimensional Schwarzschild black hole and Morris-Thorne wormhole have been found. We have assumed some candidates of dark energy like holographic dark energy, new agegraphic dark energy, quintessence, tachyon, DBI-essence, etc. The black hole mass and the wormhole mass have been calculated in term of redshift when dark matter and above types of dark energies accrete onto them separately. We have shown th…
In the present work, our main objective is to investigate the orbits of spinning test particles around a Schwarzschild black hole under the influence of a quintessence matter field (SQBH). We begin with the dynamics of the spinning test particles around SQBH which is governed by the Mathisson-Papapetrou-Dixon (MPD) equations under the pole-dipole approximation, where the gravitational field and the higher multipoles of the particle are neglected. Depending on the types of saddle points,the effective potential are classified and the possibility of chaotic orbits is discussed. The inner most sta…
Based on the 4D momentum, the influence of quintessence on the gravitational frequency shift and the deflection of light are examined in modified Schwarzschild space. We find that the frequency of photon depends on the state parameter of quintessence $w_q$: the frequency increases for $-1<w_q<-1/3$ and decreases for $-1/3<w_q<0$. Meanwhile, we adopt an integral power number $a$ ($a = 3ω_q + 2$) to solve the orbital equation of photon. The photon's potentials become higher with the decrease of $ω_q$. The behavior of bending light depends on the state parameter $ω_q$ sensitively. In particular, …
In this work, we observe that in the presence of the string cloud parameter $a$ and the quintessence parameter $γ$, with the equation of state parameter $ω_q={-2}/{3}$ the radius of the shadow of the Schwarzschild black hole increases as compared with the pure Schwarzschild black hole case. The existence of both quintessential dark energy and cloud of strings magnify the shadow size and hence the strength of the gravitational field around the Schwarzschild black hole increases. Using the data collected by the Event Horizon Telescope (EHT) collaboration for the M87* and Sgr A*, we obtain upper …
We study the properties of the null geodesics of four-dimensional Einstein-Gauss-Bonnet black holes surrounded by quintessence matter. Due to the quintessence correction, we discuss the radial and non-radial geodesics. For the case of non-radial geodesics we obtain the effective potential, the photon sphere and the impact parameter associated to the null geodesics in details. We analyze the different possible orbits of massless particles (i.e. photons) such as unstable circular orbits and unbounded orbits and investigate the role of the Gauss-Bonnet coupling $α$ and the quintessence parameter …
We study the conditions required for validity of the generalized second law in phantom dominated universe in the presence of Schwarzschild black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the generalized second law in the neighborhood of transition (from quintessence to phantom regime) time. We show that even for a constant equation of state parameter the generalized second law may be satisfied provided the temperature is not taken as de Sitter temperature. It is shown that in models with (only) a transition from quinte…
Quintessence fields, introduced to explain the speed-up of the Universe, might affect the geometry of spacetime surrounding black holes, as compared to the standard Schwarzschild and Kerr geometries. In this framework, we study the neutrino pairs annihilation into electron-positron pairs ($ν{\bar ν}\to e^-e^+$) near the surface of a neutron star, focusing, in particular, on the Schwarzschild-like geometry in presence of quintessence fields. The effect of the latter is to increase the minimum photon-sphere radius ($R_{ph}$), increasing in such a way the maximum energy deposition rate near to $R…
We employ the metric of Schwarzschild space surrounded by quintessential matter to study the trajectories of test masses on the motion of a binary system. The results, which are obtained through the gradually approximate approach, can be used to search for dark energy via the difference of the azimuth angle of the pericenter. The classification of the motion is discussed.
Viscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole's gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole's center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian f…
Weinberg's energy-momentum pseudotensor is obtained for Schwarzschild metric in harmonic coordinates. On the horizon it possesses unintegrable singularities. For this reason the total energy of a collapsar can't be obtained by integrating energy density over the system's volume. The implication for gravity theories is noted. A thought on how to choose unique energy-momentum tensor is given.
We investigate the evolution of timelike geodesic congruences, in the background of a charged black hole spacetime surrounded with quintessence. The Raychaudhuri equations for three kinematical quantities namely the expansion scalar, shear and rotation along the geodesic flows in such spacetime are obtained and solved numerically. We have also analysed both the weak and the strong energy conditions for the focusing of timelike geodesic congruences. The effect of the normalisation constant and equation of state parameter on the evolution of the expansion scalar is discussed, for the congruences…
In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev black hole). In order to demonstrate that HPM is able to yield acceptable solutions for the null-geodesics with easily computable terms, the HPM is tested for the simple examples of spherically symmetric spacetimes such as Schwarzschild and Reissner-Nordström black holes. After that, the null-geodesics of light passing the vicinity of Kiselev black hole are st…
We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for three special cases of the quintessence parameter $ ε= -1/3, -2/3$ and $-1$ are derived successfully. We show that the variation of quasinormal frequencies with charge of the black hole and the quintessential parameters. The numerical results show that quintessence field decreases oscillation frequencies of all angular momentum $l$ modes and incre…
Using distributional techniques we calculate the energy--momentum tensor of the Schwarzschild geometry. It turns out to be a well--defined tensor--distribution concentrated on the $r=0$ region which is usually excluded from space--time. This provides a physical interpretation for the curvature of this geometry.
An approach to computing, withing the framework of distribution theory, the distributional valued energy-momentum tensor for the Schwarzschild spacetime is disscused. This approach avoids the problems associated with the regularization of singularities in the curvature tensors and shares common features with the by now standard treatment of discontinuities in General Relativity. Finally, the Reissner-Nordstrom spacetime is also considered using the same approach.
