Kiselev Black Hole Research Articles

Regular black holes from Kiselev anisotropic fluid

In this paper, we investigate a generalization of Kiselev black holes by introducing a varying equation-of-state parameter for the anisotropic fluid surrounding the black hole. We extend this model by allowing w in the expression pt(r)/ρ(r)=(3w+1)/2 to vary as a function of the radial coordinate, and derive new solutions to the Einstein field equations for this configuration. In particular, we study solutions that describe regular black holes. By choosing specific forms of w(r), we obtain regular black hole solutions, and show that the matter surrounding the black hole can satisfy the weak and strong energy conditions under certain values of parameters analyzed. Due to the generality of this treatment, other categories of black holes can be obtained with particular choices of the equation-of-state parameter. Our analysis confirms that the curvature invariants associated with the regular black holes remain finite at the origin, indicating the absence of singularities. We also explore the physical properties of the matter associated with these solutions. Due to its versatility, we suggest the possibility of using this approach as a tool to construct new physical solutions associated with regular black holes or other geometries of interest.

Circular motion and collisions of spinning test particles around Kerr–Kiselev black holes

Exploring the effect of exotic fields around black holes on particle dynamics may help to understand the nature of dark matter and energy. The quintessential field can be treated as one of such fields. In this work, we investigate the motion of spinning particles in the vicinity of rotating black holes immersed in quintessential dark energy, characterized by the equation of state (EoS) parameter ω∈(−1;−1/3) governing the equation of state of the dark energy and dimensionless quintessential field parameter C. Using the Mathisson–Papapetrou–Dixon (MPD) equations, we derive the effective potential and study superluminal bound values for the particle spin. Also, we investigate the behaviors of the innermost and outermost stable circular orbit (ISCO & OSCO) of spinning test particles and their energy and angular momentum at the orbits. Note that the OSCO exists due to the third cosmological-like horizon caused by the quintessential field and shows that the ISCO and OSCO coincide at critical values of the quintessential field and EoS parameters, which also depend on the particle and black hole spin. Finally, we explore collisions of spinning particles and analyze the center-of-mass energies and critical angular momentum, which allows the collisions of the particles near the black hole.

Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center-of-mass energy, Penrose-process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value aE. Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter γ. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter γ and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and γ the ISCO becomes larger than that for the Kerr spacetime. For the center-of-mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose-process is more efficient for smaller values of the string cloud parameter b and the parameter γ has no significant impact on this process. Moreover we see that an increase in the parameters b, γ and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, γ and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.

Rotating kiselev black holes in f(R, T) gravity

Exact solutions describing rotating black holes can provide significant opportunities for testing modified theories of gravity, which are motivated by the challenges posed by dark energy and dark matter. Starting with a spherical Kiselev black hole as a seed metric, we construct rotating Kiselev black holes within the f(R, T) gravity framework using the revised Newman-Janis algorithmthe f(R, T) gravity-motivated rotating Kiselev black holes (FRKBH) with additional parameter quintessence parameter ω and state parameter γ, apart from mass M and spin a, which encompasses, as exceptional cases, Kerr (K = 0) and effective Kerr-Newman (K = Q 2) black holes. These solutions give rise to distinct classes of black holes surrounded by fluids while considering specific values of the w for viable choices for the f(R, T) function. From the parameter space or domain of existence of black holes defined by a and γ for FKRBH, we discover that when a 1 < a < a 2, there is a critical value γ = γ E which corresponds to extreme value black holes portrayed by degenerate horizons. When a < a 1 (a > a 2), we encounter two distinct critical values γ = γ E1, γ E2 with γ E1 > γ E2 (or γ = γ E3, γ E4 with γ E3 > γ E4). We discuss the horizon and global structure of FKRBH spacetimes and examine their dependence on parameters w and γ. This exploration is motivated by the remarkable effects of f(R, T) gravity, which gives rise to diverse and intricate spacetime structures within the domain where black holes exist.

Probing the Bardeen–Kiselev black hole with the cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds

In this work, we investigate a static and spherically symmetric Bardeen–Kiselev black hole (BH) with the cosmological constant, which is a solution of the Einstein-non-linear Maxwell field equations. We compute the quasinormal frequencies for the Bardeen–Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations. By varying the BH parameters, we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner–Nordström–de Sitter BH surrounded by quintessence (RN-dSQ). Interestingly, it is shown that the responses of the Bardeen–Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q, the state parameter w and the normalization factor c are varied; however, for the gravitational perturbations, the responses of the Bardeen–Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied. Therefore, compared with the gravitational perturbations, the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately. Another interesting observation is that, due to the presence of Kiselev quintessence, the electromagnetic perturbations around the Bardeen–Kiselev BH with the cosmological constant damps faster and oscillates slowly; for the gravitational perturbations, the quasinormal mode decays slowly and oscillates slowly. We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen–Kiselev BH with the cosmological constant; it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.

Gravitational wave pulse and memory effects for hairy Kiselev black hole and its analogy with Bondi–Sachs formalism

The investigation of non-vacuum cosmological backgrounds containing black holes is greatly enhanced by the Kiselev solution. This solution plays a crucial role in understanding the properties of the background and its relationship with the features of the black hole. Consequently, the gravitational memory effects at large distances from the black hole offer a valuable means of obtaining information about the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole. This paper investigates the gravitational memory effects in the context of the Kiselev solution through two distinct approaches. At first, the gravitational memory effect at null infinity is explored by utilizing the Bondi–Sachs formalism by introducing a gravitational wave (GW) pulse to the solution. The resulting Bondi mass is then analyzed to gain further insight. Therefore, the Kiselev solution is being examined to determine the variations in Bondi mass caused by the pulse of GWs. The study of changes in Bondi mass is motivated by the fact that it is dynamic and time-dependent, and it measures mass on an asymptotically null slice or the densities of energy on celestial spheres. In the second approach, the investigation of displacement and velocity memory effects is undertaken in relation to the deviation of two neighboring geodesics and the deviation of their derivative influenced by surrounding field parameter N and the hair of hairy Kiselev black hole. This analysis is conducted within the context of a GW pulse present in the background of a hairy Kiselev black hole surrounded by a field parameter N.

Impact of charged and quantum-correction on the dynamics of scalar shell surrounded by Kiselev black hole

The objective of this study is to investigate the geometric configurations of a thin-shell in the framework of quantum-corrected charged Kiselev black holes. In order to do this, a cut and paste technique is employed to align the inner Minkowski spacetime with the black hole solutions under consideration. Our research explores the effects of quantum-correction on the stability of thin-shell using linearized radial perturbation method incorporating the phantomlike equation of state such as quintessence. This approach allows for the identification of stable configurations of the thin-shell situated beyond the expected location of the event horizon in the exterior manifold. Moreover, it is evident that the stability of the thin-shell is significantly dependent on the parameters associated with the black hole solutions. In this study, we investigate the dynamics of the thin-shell configuration using Klein–Gordon’s equation of motion, including both massive and massless scalar fields. The results of our study suggest that the presence of the scalar field has a significant impact on the behavior of the thin-shell, resulting in notable phenomena such as expansion and collapse. The aforementioned results provide valuable insights into the behavior of black hole solutions by examining the dynamics of thin-shells in relation to quantum-correction parameters involving scalar fields. In summary, it is observed that the presence of a quantum-correction parameter has the effect of reducing the stable configuration of a Kiselev black holes.

Test particles and quasiperiodic oscillations around Kiselev black hole with cloud of strings* *Supported by the F-FA-2021-510 Grant of the Ministry of Innovative Development of Uzbekistan

In the present study, we investigate the dynamics of test particles around a Schwarzschild black hole surrounded by quintessence and immersed in a scalar string cloud field. We start our study by defining the possible values of the quintessence and cloud of string parameters corresponding to the existence of the black hole horizon for fixed values of the parameters of the equation of state for dark energy. We also study the effects of the effective potential on the circular motion, energy, and angular momentum of the test particles together with the innermost stable circular orbits (ISCOs). We investigate the fundamental frequencies in the particle oscillations along stable circular orbits. We relate the stability of the orbits to the Lyapunov exponent, and the chaotic behavior is studied graphically. Finally, we apply the fundamental frequencies to describe quasiperiodic oscillations (QPOs) and find that, in the presence of both fields, low-frequency twin-peak QPOs are not observed. In addition, we obtain the constraint values for the string cloud parameter and mass of the black hole candidates located in the center of the microquasars GRO J1655-40 and GRS 1915+105 as well as the Milky Way galaxy.

Investigation on the stability and quantum phase transition of the charged rotating Kiselev Black Hole embedded in Quintessence field with quantum fluctuation of entropy

Immediate local impacts of cosmic acceleration upon a rapidly rotating black hole are very interesting in recent studies. In this paper, the stability of a rapidly rotating black hole and the minimum value of the ratio between the black hole’s angular momentum to it’s mass which ensures the stability, are investigated simultaneously. Also, two modern forms of uncertainty relations are proposed by enhancing the usual Heisenberg algebra with superior terms, in order to supervise on thermodynamic properties of the rotating black hole. An asymptotically flat Kiselev black hole solution, cultivated by quintessence field is chosen for this purpose. The local shifts in spacetime geometry next to the rotating black hole can be resolved from a modified metric, occupying the surrounding spacetime of the black hole. The angular momentum of a rotating black hole depends on the rate of change in acquiring mass by it. On the other hand, at the same time, due to the effect of the quintessence field, there exists repulsive gravitational force inside the black hole. So, there is an uncertainty in the position of innermost stable circular orbit as well as radius of the rotating black hole. This uncertainty is also investigated in our work. Relying on two new forms of uncertainty principle, the modified thermodynamic variables like black hole’s Hawking temperature, heat-capacity, entropy at the black hole’s event horizon, etc. are computed under rotation. Quantum corrections of black hole’s Hawking temperature, entropy, free-energy, etc. are also explored. Further, quantum corrected heat capacity of the rotating black hole is studied and also thermal stability is inquired. The existence of transitions of phase in case of a rapidly rotating black hole are also found out. Again, quantum corrected entropy of black hole contains logarithmic terms and their effects on thermal stability of the rotating black hole are also discussed. Modifications in the mass-temperature, specific heat, etc. of a rotating black hole are also presented according to the modified extension parameters.

Reduced Kiselev black hole

The Kiselev model describes a black hole surrounded by a fluid with equations of state p_r/rho =-1 and p_t/rho =(3w+1)/2 respectively in radial and tangential directions. It has been extensively studied in the parameter region -1<w<-1/3. If one rids off the black hole and turns to the region -1/3<w<0, i.e. p_t>0, then a new horizon of black hole type will emerge. This case has been mentioned in Kiselev’s pioneer work but seldom investigated in the literature. Referring to it as reduced Kiselev black hole, we revisit this case with attention to its causal structure, thermodynamics, shadow cast and weak-field limit. An alternative interpretation and extensions of the black hole are also discussed.

Thermodynamic product formulae for Finslerian Kiselev black hole

The main goal of this paper is to solve the Finslerian Kiselev black hole and investigate its thermodynamic characteristics surrounded by dust, radiation, quintessence, and the cosmological constant. Since these black holes have multiple horizons, thus we calculate thermodynamic quantities, including area, horizon radius, Bekenstein–Hawking entropy, Hawking temperature, surface gravity, and Komar energy products. In addition, we study all universal relations of these black holes and discuss the role and effect of the Finslerian Ricci scalar (eta ) on Finslerian Kiselev black holes and their stability.

Probing dark fluids and modified gravity with gravitational lensing

ABSTRACT We generalize the result of Rindler-Ishak for the lensing deflection angle in a Schwarzschild–deSitter (SdS) space–time, to the case of a general spherically symmetric fluid beyond the cosmological constant. We thus derive an analytic expression to first post-Newtonian order for the lensing deflection angle in a general static spherically symmetric metric of the form $\mathrm{ d}s^2 = f(r)\mathrm{ d}t^{2} -\frac{\mathrm{ d}r^{2}}{f(r)}-r^{2}(\mathrm{ d}\theta ^2 +\sin ^2 \theta \mathrm{ d}\phi ^2)$ with $f(r) = 1 - \frac{2m}{r}-\sum _{i} b_\mathrm{ i}\,\, r_0^{-q_i}\,\, \left(\frac{r_0}{r}\right)^{q_i}$, where r0 is the lensing impact parameter, $b_i\ll r_0^{q_i}$, m is the mass of the lens, and qi are real arbitrary constants related to the properties of the fluid that surrounds the lens or to modified gravity. This is a generalization of the well known Kiselev black hole metric. The approximate analytic expression of the deflection angle is verified by an exact numerical derivation and in special cases it reduces to results of previous studies. The density and pressure of the spherically symmetric fluid that induces this metric is derived in terms of the constants bi. The Kiselev case of a Schwarzschild metric perturbed by a general spherically symmetric dark fluid (e.g. vacuum energy) is studied in some detail and consistency with the special case of Rindler-Ishak result is found for the case of a cosmological constant background. Observational data of the Einstein radii from distant clusters of galaxies lead to observational constraints on the constants bi and through them on the density and pressure of dark fluids, field theories, or modified gravity theories that could induce this metric.

Kiselev and Schwarzschild–de Sitter black holes in higher derivative theories of gravitation

We consider the influence of the higher-order correction to the gravitational action inspired by the Goroff-Sagnotti term upon the Kiselev black hole with $\stackrel{\texttildelow{}}{\ensuremath{\omega}}=\ensuremath{-}2/3$ and contrast the thus obtained results with the analogous results obtained for the Schwarzschild--de Sitter black hole. Expressing the perturbed solution in terms of the exact radius of the event horizon and the radius of the cosmological horizon of the unperturbed black hole we calculate corrections to the line element, to the cosmological horizon, and to the surface gravity. It is shown that although in both cases the lukewarm configuration does not exist classically (the equality of the surface gravities is possible only for the merged horizons), the sixth-order term removes the degeneracy of the classical solution and simultaneously shifts the degenerate horizon to a new place in the space of parameters. The lukewarm configuration is characterized by the value of the parameters that classically characterize the extremal solution. It is shown that the Karlhede scalar still may serve as the detector of the event and the cosmological horizon. Finally, we study the complex frequencies of the low-lying fundamental modes of the quasinormal oscillations and argue that they are the best candidates (at least theoretically) to distinguish between different black hole configurations.

Observable features of charged Kiselev black hole with non-commutative geometry under various accretion flow

The light passing near the black hole (BH) is deflected due to the gravitational effect, producing the BH shadow, a dark inner region that is often surrounded by a bright ring, whose optical appearance comes directly from BH’s mass and its angular momentum. We mainly study the shadow and observable features of non-commutative (NC) charged Kiselev BH, surrounded by various profiles of accretions. To obtain the BH shadow profile, we choose specific values of the model parameters and concluded that the variations of each parameter directly vary the light trajectories and size of BH. For thin disk accretion, which includes direct lensing and photon rings emissions, we analyze that the profile of BH contains the dark interior region and bright photon ring. However, their details depends upon the emissions, generally, direct emission plays significant role in the total observed luminosity, while lensing ring has a small contribution and the photon ring makes a negligible contribution, as usual, the latter can be ignored safely. Moreover, we also consider the static and infalling accretion matters and found that the location of the photon sphere is almost the same for both cases. However, the specific intensity which is observed from BH profile found to be darker for infalling accretion case due to the Doppler effect of the infalling motion as compared to the static one.

Simulated image of the shadow of the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity with a thin accretion disk

Simulated image of the shadow of the Kerr–Newman–NUT–Kiselev black hole in the Rastall gravity with a thin accretion disk

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma* *Partly supported by the Uzbekistan Ministry for Innovative Development (FZ-20200929344 and F-FA-2021-510). I.H. is grateful to the Institute of Mathematics, University of Aberdeen, Scotland, UK, where a part of this study was done under the IMU-CDC Individual Travel Support Program. G.M. is supported

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.

Deflection and gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit

In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter ω and the matter amount parameter α. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case (−1/3 < ω < 0) the deflection angles are expressable as quasi-power series of the dimensionless quantities M/b, b/r s,d and α/M 1+3ω where M, b, r s,d are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of (−1 < ω < −1/3), but with the closest radius r 0 replacing b. In the asymptotically flat (or non-flat) case, the increase of α or decrease of ω will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing α or decreasing ω will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing α or ω will both lead to smaller apparent angles.

Energy extraction via magnetic reconnection in Lorentz breaking Kerr–Sen and Kiselev black holes

Black holes can accumulate a large amount of energy, responsible for highly energetic astrophysical phenomena. Although the Blandford–Znajek is considered to date the leading mechanism for powering jets and GRBs, recently fast magnetic reconnection (MR) of the magnetic field was proposed as a new way to extract energy. In this paper, we investigate this phenomena in a bumblebee Kerr–Sen BH, which differentiates from standard Kerr solution via a Lorentz symmetry breaking parameter ell and an electric charge one b. We find that the presence of the charge parameter strongly changes the simple Kerr case, making this extraction mechanism possible even for not extremely rotating black holes (asim 0.7). We also show that, under appropriate circumstances, MR is more efficient compared to the Blandford–Znajek mechanism. We finally compare these results with dark energy (quintessence) black-hole solutions. In this case, we find that a Kerr black hole is indistinguishable from a rotational Kiselev one, whatever the energy-matter that surrounds it (including ordinary matter, such as dust and radiation).

Chaos bound and its violation in charged Kiselev black hole

The chaos bound in the near-horizon regions has been studied through the expansions of the metric functions on the horizon. In this paper, we investigate the chaos bound in the near-horizon region and at a certain distance from the horizon of a charged Kiselev black hole. The value of the Lyapunov exponent is accurately calculated by a Jacobian matrix. The angular momentum of a charged particle around the black hole affects not only the exponent, but also the position of the equilibrium orbit. This position gradually moves away from the horizon with the increase of the angular momentum. We find that the bound is violated at a certain distance from the horizon and there is no violation in the near-horizon region when the charge mass ratio of the particle is fixed. The small value of the normalization factor is more likely to cause the violation.

Rotating charged black hole shadow in quintessence

We analytically study the shadow of the charged rotating black hole in the presence of quintessence. The quintessential energy adequately affects the shape and size of the black hole shadow. The shadow of a rotating black hole spots a distorted dark disk. The shape and size of the black hole shadow depend on its mass M, spin parameter a, charge q, quintessential field parameter ωq, and normalization factor c. We derive the entire geodesic structure of photons near black holes using the Hamilton–Jacobi equation and Carter constant separable method. We relate the celestial coordinates to geodesic equations and plot the contour of the black hole shadow for the case ωq=−2/3. To find the effect of quintessential energy on the black hole shadow, we obtain observable i.e. shadow radius Rs and distortion parameter δs. We compare all our results with the Kerr black hole in quintessence, Kerr–Newman black hole and Bardeen–Kiselev black hole. Our study shows that for a fixed value of the spin parameter a and normalization factor c, the black hole shadow monotonically decreases and gets more distorted with charge q.