In the present work, we study the general surrounded Vaidya solution by the various cosmological fields and its nature describing the possibility of the formation of naked singularities or black holes. Motivated by the fact that real astrophysical black holes as non-stationary and non-isolated objects are living in non-empty backgrounds, we focus on the black hole subclasses of this general solution describing a dynamical evaporating-accreting black holes in the dynamical cosmological backgrounds of dust, radiation, quintessence, cosmological constant-like and phantom fields, the so called surrounded Vaidya black hole. Then, we analyze the timelike geodesics associated with the obtained surrounded black holes and we find that some new correction terms arise relative to the case of Schwarzschild black hole. Also, we address some of the subclasses of the obtained surrounded black hole solution for both dynamical and stationary limits. Moreover, we classify the obtained solutions according to their behaviors under imposing the positive energy condition and discuss how this condition imposes some severe and important restrictions on the black hole and its background field dynamics.
We study the thermodynamical features and dynamical evolutions of various apparent horizons associated with the Vaidya evaporating black hole surrounded by the cosmological fields of dust, radiation, quintessence, cosmological constant-like and phantom. In this regard, we address in detail how do these surrounding fields contribute to the characteristic features of a surrounded dynamical black hole in comparison to a dynamical black hole in an empty background.
We study the Vaidya black hole surrounded by the exotic quintessence-like, phantom-like and cosmological constant-like fields by means of entropic considerations. Explicitly, we show that for this thermodynamical system, the requirement for the identification of D-bound and Bekenstein entropy bound can be considered as a thermodynamical criterion by which one can rule out the quintessence-like and phantom-like fields, and prefer the cosmological constant as a viþable cosmological field.
Hawking Radiation and Second-Order Quantum Corrected Thermodynamics with Black Hole Remnant Formation in a Vaidya-Bonnor Black Hole Surrounded by Quintessence
University of Maroua（马里瓦大学）；Higher Teachers’ Training College, University of Maroua（马里瓦大学高等师资培训学院）；University of Yaounde I（雅温得第一大学）；Ruhr-Universität Bochum（波鸿鲁尔大学）；National Advanced School of Engineering, University of Yaoundé I（雅温得第一大学国立高级工程学院）；Botswana International University of Science and Technology（博茨瓦纳科学技术大学）
A recently proposed approach to the construction of the Vaidya metric in double-null coordinates for generic mass functions is extended to the $n$-dimensional $(n>2)$ case and to allow the inclusion of a cosmological constant. The approach is based on a qualitative study of the null-geodesics, allowing the description of light-cones and revealing many features of the underlying causal structure. Possible applications are illustrated by explicit examples. Some new exact solutions are also presented and discussed. The results presented here can simplify considerably the study of spherically symm…
The spacetimes for Vaidya's radiating stellar exterior and Kinnersley's photon rocket in a cosmological background are obtained by performing the same conformal transformation as is used to obtain the Robertson-Walker metric from Minkowski spacetime. In the case of the cosmological radiating stellar exterior, a two-fluid solution is found that obeys all of the energy conditions and consists of a null fluid and a perfect fluid that asymptotically falls off to the standard cosmological values for pressure and density at infinite radius. For the cosmological photon rocket, the massless case is fi…
A magnetic-monopole solution of a non-Abelian gauge theory as proposed by 't Hooft and Polyakov is studied in the Vaidya spacetime. We find that the solutions of Einstein equations generates a geometry of the Bonnor-Vaidya corresponding to magnetically charged null fluid with Higgs field contributing a cosmological term. In the absence of the scalar fields the corresponding Wu-Yang solution of the gauge theory still generates the Bonnor-Vaidya geometry, but with no cosmological term.
We present here the field equations describing a non-stationary spherically symmetric n-dimensional charged black hole with varying mass m(v) and/or electric charge q(v), described by a generic charged Vaidya metric with cosmological constant Lambda in double null coordinates. This formulation of the metric has been shown to be particularly useful for perturbative studies and it was used in some recent works. Here we also discuss some issues related to the apparent and event horizons of the black hole.
We study Hawking radiation and $P-v$ criticality of charged dynamical (Vaidya) black hole in Anti-de Sitter (AdS) space. By investigating the near horizon properties of scalar field, we derive Hawking temperature of dynamical charged (Vaidya) AdS black hole. Based on this result, by regarding the cosmological constant as the thermodynamic pressure, we investigate the analogy between the charged dynamical (Vaidya) AdS black holes in the ensemble with the fixed charge and van der Waals liquid-gas system in detail, including equation of state, $P-v$ diagram, critical point, heat capacities and cr…
In this paper,we discuss optical properties of the nonlinear magnetic charged black hole surrounded by quintessence with a non-zero cosmological constant $Λ$. Setting the state parameter $ω=-3/2$ , we studied the horizon, the photon region and the shadow of this black hole. It turned out that for a fixed quintessential parameter $γ$, in a certain range, with the increase of the rotation parameter $a$ and magnetic charge $Q$, the inner horizon radius increases while the outer horizon radius decreases. And the cosmological horizon $r_Λ$ decrease when $γ$ or $Λ$ incease and increase slightly with…
The cosmological candidate fields for dark energy as quintessence, phantom and cosmological constant, are studied in terms of an entropic hypothesis imposed on the McVittie solution surrounded by dark energy. We certify this hypothesis as "$D$-bound-Bekenstein bound identification" for dilute systems and use it as a criterion to determine which candidate of dark energy can satisfy this criterion for a dilute McVittie solution. It turns out that only the cosmological constant can pass this criterion successfully while the quintessence and phantom fields fail, as non-viable dark energy fields fo…
We consider non-stationary spherically symmetric $n$-dimensional charged black holes with varying mass $m(v)$ and/or electric charge $q(v)$, described by generic charged Vaidya metrics with cosmological constant $Λ$ in double null coordinates, and perform a comprehensive numerical analysis of the fundamental quasinormal modes (QNM) for minimally coupled scalar fields. We show that the "instantaneous" quasinormal frequencies exhibit the same sort of non-stationary behavior reported previously for the four-dimensional uncharged case with $Λ=0$. Such property seems to be very robust, independent …
In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the RN-AdS black hole surrounded by the quintessence under the scattering of a charged complex scalar field. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. In the normal phase space, the cosmological constant and th…
We study a class of charged cosmological black holes defined by the Shah-Vaidya solution, which is similar to the McVittie solution but for a central object of nonzero electric charge. We show that the Shah-Vaidya metric is a solution of Einstein's equations with a cuscuton and a Maxwell fields as sources, as well as a mass parameter. We then analyze the possible causal structures of the solution under some few physically reasonable assumptions, and determine the regions in the parameter space corresponding to well behaved charged cosmological black holes and those corresponding to naked singu…
We study global defects coupled to higher-dimensional gravity with a negative cosmological constant. This paper is mainly devoted to studying global black brane solutions which are extended global defects surrounded by horizons. We find series solutions in a few separated regions and confirm numerically that they can be mutually connected. When the world volume of the brane is Ricci-flat, the brane is surrounded by a degenerated horizon, while it is surrounded by two horizons when the world volume has a positive constant curvature. Each solution corresponds to an extremal and a non-extremal st…
In this work, we obtain uncharged\charged Kiselev-like black holes as a new class of black hole solutions surrounded by perfect fluid in the context of Rastall theory. Then, we study the specific cases of the uncharged\charged black holes surrounded by regular matter like dust and radiation, or exotic matter like quintessence, cosmological constant and phantom fields. By comparing the Kiselev-like black hole solutions in Rastall theory with the Kiselev black hole solutions in GR, we find an effective perfect fluid behaviour for the black hole's surrounding field. It is shown that the correspon…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe may undergo a topology change and in between is a mixture of two different Friedmann-Rob…
In this work we study the phase transition of the charged-AdS black hole surrounded by quintessence via an alternative extended phase space defined by the charge square $Q^2$ and her conjugate $Ψ$, a quantity proportional to the inverse of horizon radius, while the cosmological constant is kept fixed. The equation of state is derived under the form $Q^2=Q^2(T,Ψ)$ and the critical behavior of such black hole analyzed. In addition, we explore the connection between the microscopic structure and Ruppeiner geothermodynamics. We also find that, at certain points of the phase space, the Ruppeiner cu…
The quantum stress-energy tensor of a massless scalar field propagating in the two-dimensional Vaidya-de Sitter metric, which describes a classical model spacetime for a dynamical evaporating black hole in an inflationary universe, is analyzed. We present a possible way to obtain the Hawking radiation terms for the model with arbitrary functions of mass. It is used to see how the expansion of universe will affect the dynamical process of black hole evaporation. The results show that the cosmological inflation has an inclination to depress the black hole evaporation. However, if the cosmologica…
We derive the matching conditions between FLRW and generalised Vaidya spacetimes with spherical, planar or hyperbolic symmetry, across timelike hypersurfaces. We then construct new models of gravitational collapse of FLRW spacetimes with a negative cosmological constant having electromagnetic radiation in the exterior. The final state of the collapse are asymptotically AdS black holes with spherical, toroidal or higher genus topologies. We analyse the collapse dynamics including trapped surface formation, for various examples.
We obtain an exact solution of Einstein's equations for a charged, static and spherically symmetric body, surrounded by a fluid of strings and with a cosmological constant. This corresponds to the Reissner-Nordström (de Sitter)-Anti de Sitter black hole surrounded by a fluid of strings. Some aspects concerning the horizons and geodesic motion are discussed. We also obtain the metric corresponding to the Kerr-Newman black hole surrounded by a fluid of strings, by using a method to construct the rotating solution from its counterpart static one. The horizons, ergoregions, and geodesic motion are…
Inspired in a previous work by McClure and Dyer (Classical Quantum Gravity 23, 1971 (2006)), we analyze some solutions of the Einstein-Maxwell equations which were originally written to describe charged black holes in cosmological backgrounds. A detailed analysis of the electromagnetic sources for a sufficiently general metric is performed, and then we focus on deriving the electromagnetic four-current as well as the conserved electric charge of each metric. The charged McVittie solution is revisited and a brief study of its causal structure is performed, showing that it may represent a charge…
Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from non-singular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities. If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces. Unlike the original Penrose's theorem, our theorems provi…
Here we derive the mass formulae for a cylindrical black hole solution with positive cosmological constant and surrounded by dust. The expressions are generalising those found by Smarr for the mass and momentum of a Kerr black hole.
In this paper, we investigate the geodesic motion of massive and massless test particles in the vicinity of a black hole space-time surrounded by perfect fluid (quintessence, dust, radiation, cosmological constant and phantom) in Rastall theory. We obtain the full set of analytical solutions of the geodesic equation of motion in the space-time of this black hole. For all cases of perfect fluid, we consider some different values of Rastall coupling constant $kλ$ so that the equations of motion have integer powers of $\tilde{r}$ and also can be solved analytically. These analytical solutions are…
Considering a Vaidya exterior spacetime, we study dynamical models of prototype gravastars, made of an infinitely thin spherical shell of a perfect fluid with the equation of state $p = σ$, enclosing an interior de Sitter spacetime. We show explicitly that the final output can be a black hole, an unstable gravastar, a stable gravastar or a "bounded excursion" gravastar, depending on how the mass of the shell evolves in time, the cosmological constant and the initial position of the dynamical shell. This work presents, for the first time in the literature, a gravastar that emits radiation.
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…
Due to the gravitational lensing effect, a black hole casts a shadow larger than its horizon over a bright background, and the shape and size can be calculated. The Event Horizon Telescope collaboration has produced the first direct image (shadow) of the black hole and it is in accordance with the shadow of a Kerr black hole of general relativity. However, deviations from the Kerr black hole arising from modified theories of gravity are not ruled out and they are important as they offer an arena to test these theories through astrophysical observation. This stimulates us to investigate rotatin…
In this paper, we test the weak cosmic censorship conjecture (WCCC) for the Reissner-Nordström-de Sitter (RN-dS) black hole surrounded by perfect fluid dark matter. We consider a spherically symmetric perturbation on deriving linear and non-linear order perturbation inequalities by applying new version of gedanken experiments well accepted from the work of Sorce and Wald. Contrary to the well-known result that the Reissner-Nordström (RN) black hole could be overcharged under linear order particle accretion it is hereby shown that the same black hole in perfect fluid dark matter with cosmologic…
In the present paper, we investigate the required anisotropy of an exact regular Bardeen black hole characterized by its mass $M$, the nonlinear parameter $g$, the quintessence field parameter $a$ in anti-de sitter spacetime with a static quintessence matter field. We also show that the relative pressure anisotropy, equation of state and the pressure depends on radial coordinate, reflecting the required anisotropy for Bardeen black hole in the quintessence background. Next, we analyze the Joule-Thompson ($JT$) expansion of the black hole spacetime. Treating the cosmological constant as thermod…
The Raychaudhuri equation for null rays is a powerful tool for finding consistent embeddings of cosmological bubbles into a background spacetime in a way that is largely independent of the matter content. We find that spatially flat or positively curved thin wall bubbles surrounded by a cosmological background must have a Hubble expansion that is either contracting or expanding slower than the background, which are more stringent constraints than those obtained by the usual Israel thin-wall formalism. Similarly, a cosmological bubble surrounded by Schwarzschild space, occasionally used as a si…
In this work we analyze a solution that mimics the Bardeen solution with a cosmological constant surrounded by quintessence. We show that this solution can be obtained by Einstein equations coupled with nonlinear electrodynamics. We also show that the solution is not always regular and what the conditions for regularity are. We analyze the thermodynamics associated with this type of solution by establishing the form of the Smarr formula and the first law of thermodynamics. We obtain some thermodynamic quantities such as pressure, temperature, heat capacity and isothermal compressibility. Once …
Considering the variable cosmological constant in the extended phase space has a significant background in the black hole physics. It was shown that the thermodynamic behavior of charged AdS black hole surrounded by the quintessence in the extended phase space is similar to the van der Waals fluid. In this paper, we indicate that such a black hole admits the same criticality and van der Waals like behavior in the non-extended phase space. In other words, we keep the cosmological constant as a fixed parameter, and instead, we consider the normalization factor as a thermodynamic variable. We sho…
In this paper we analyze the propagation of a charged scalar field in a Reissner-Nordström black hole endowed with one anisotropic fluid that can play the role of a cosmological term for certain set of parameters. The evolution of a scalar wave scattering is examined giving rise to the same superradiant scattering condition as in the de Sitter case. In addition, an analysis of the modes coming from the application of quasinormal boundary conditions is presented. Some special cases displaying analytical solutions for the quasinormal frequencies are discussed. Moreover, the superradiant conditio…
The black hole solutions in higher-dimensional spacetimes with the presence of the power-Maxwell field, surrounded by quintessence, are investigated for Einstein as well as Rastall gravity. The obtained solutions accommodate for spherical, planar and hyperbolic symmetries with the presence of the cosmological constant. Besides, we show that several known black hole solutions in literature such as those for linear Maxwell theory and BTZ black hole can be obtained as special cases. The implications of Rastall's theory related to the present study and the thermodynamics of the black hole solution…
In this paper we investigate circular orbits for test particles around Schwarzschild-de Sitter (dS) black hole surrounded by perfect fluid dark matter. We determine the region of circular orbits bounded by innermost and outermost stable circular orbits. We show that the impact of the perfect fluid dark matter shrinks the region where circular orbits can exist as the values of both innermost and outermost stable circular orbits decrease. We find that for specific lower and upper values of dark matter parameter there exist double matching values for inner and outermost stable circular orbits. It…
Modifying the Kerr-Schild transformation used to generate black and white hole spacetimes, new dynamic black and white holes are obtained using a time-dependent Kerr-Schild scalar field. Physical solutions are found for black holes that shrink with time and for white holes that expand with time. The black hole spacetimes are physical only in the vicinity of the black hole, with the physical region increasing in radius with time. The white hole spacetimes are physical throughout. Unlike the standard Schwarzschild solution the singularities are non-isolated, since the time-dependence introduces …
We consider Reissner-Nordström black holes surrounded by quintessence where both a non-extremal event horizon and a cosmological horizon exist besides an inner horizon ($-1\leq ω<-1/3$). We determine new extreme black hole solutions that generalize the Nariai horizon to asymptotically de Sitter-like solutions for any order relation between the squares of the charge $q^2$ and the mass parameter $M^2$ provided $q^2$ remains smaller than some limit, which is larger than $M^2$. In the limit case $q^2=9ω^2 M^2/(9ω^2-1)$, we derive the general expression of the extreme cosmo-black-hole, where the th…
We investigate extremal electrically charged black holes in Einstein-Maxwell-dilaton theory with a cosmological constant inspired by string theory. These solutions are not static, and a timelike singularity eventually appears which is not surrounded by an event horizon. This suggests that cosmic censorship may be violated in this theory.
As a local effect of dynamical dark energy, bending of light in the presence of a spherically symmetric and static black hole surrounded by quintessence has been studied. Having in mind recent observational data, we have treated the problem as a deviation from Kottler space-time. This deviation is measured by a perturbation parameter $\varepsilon$ included in the equation of state parameter of quintessence as $ω_q=-1+\frac{1}{3}\varepsilon$. Here, the deflection angle is calculated and then the result is compared with \cite{Arakida:2011th} in the limit $\varepsilon\rightarrow 0$ where the quin…
Using Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum complexes we explicitly evaluate the energy and momentum distributions associated with a non-static and circularly symmetric three-dimensional spacetime. The gravitational background under study is an exact solution of the Einstein's equations in the presence of a cosmological constant and a null fluid. It can be regarded as the three-dimensional analogue of the Vaidya metric and represents a non-static spinless (2+1)-dimensional black hole with an outflux of null radiation. All four above-mentioned prescriptions give exa…
Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic …
