We use the canonical energy method of Hollands and Wald to study the stability properties of asymptotically flat, stationary solutions to a very general class of theories, consisting of a set of coupled scalar fields and p-form gauge fields, minimally coupled to gravity. We find that, provided certain very weak assumptions are made on the coupling coefficients, the canonical energy method can be extended to this class of theories. In particular, we construct a quadratic form E on initial data perturbations, with the properties that E > 0 on all perturbations indicates stability, while E < 0 on some perturbation indicates instability. Furthermore, we show that the conditions needed for the existence of E allow for a stable definition of asymptotic flatness. Finally, we extend the proof of the Gubser-Mitra conjecture, given by Hollands and Wald, to this class of theories. In particular, this shows that for sufficiently extended, charged black brane solutions to such theories, thermodynamic instability implies dynamical instability.
We examine the stability of extremal braneworld Reissner-Nordström black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.
We numerically study the superradiant instability of charged massless scalar field in the background of charged stringy black hole with mirror-like boundary condition. We compare the numerical result with the previous analytical result and show the dependencies of this instability upon various parameters of black hole charge $Q$, scalar field charge $q$, and mirror radius $r_m$. Especially, we have observed that imaginary part of BQN frequencies grows with the scalar field charge $q$ rapidly.
We examine the stability of charged Lovelock black hole solutions under vector type and scalar type perturbations. We find the suitable master variables for the stability analysis; the equations for these variables are the Schrodinger type equations with two components and these Schrodinger operators are symmetric. By these master equations, we show that charged Lovelock Black holes are stable under vector type perturbations. For scalar type perturbations, we show the criteria for the instability and check these numerically. In our previous paper, we have shown that nearly extremal black holes…
We study the instability of the charged Gauss-Bonnet de Sitter black holes under gravito-electromagnetic perturbations. We adopt two criteria to search for an instability of the scalar type perturbations, including the local instability criterion based on the $AdS_2$ Breitenlöhner-Freedman (BF) bound at extremality and the dynamical instability via quasinormal modes by full numerical analysis. We uncover the gravitational instability in five spacetime dimensions and above, and construct the complete parameter space in terms of the ratio of event and cosmological horizons and the Gauss-Bonnet c…
We study the Gregory-Laflamme instability of 5D compactified, electrically charged black strings. We consider static, linear perturbations of these solutions and derive master equation for these perturbations. Using numerical analysis we search for the threshold unstable modes and derive the critical wave-length. The results are illustrated in the black string mass v.s. electric charge phase diagram. Similar diagram is constructed using global thermodynamic equilibrium argument applied to the charged string and 5D electrically charged black hole. The results derived illustrate that electric ch…
We study the effect of R**2 term to the modulated instability in the U(1) charged black hole in five-dimensional Anti-de Sitter space-time. We consider the first-order corrections of R**2 term to the background and the linear order perturbations in the equations of motion. From the analysis, we clarify the effect of R**2 term in the modulated instability, and conclude that fluctuations are stable in the whole bulk in the range of values the coefficient of R**2 term can take.
We study the instability of near extremal and extremal four-dimensional AdS charged hairy black hole to radial neutral massive and charged massless scalar field perturbations. We solve the scalar field equation by using the improved asymptotic iteration method and the time domain analysis and we find the quasinormal frequencies. For the charged scalar perturbations, we find the superradiance condition by computing the reflection coefficient in the low-frequency limit and we show that in the superradiance regime, which depends on the scalar hair charge, all modes of radial charged massless pert…
We consider scalar field perturbations of the asymptotically Gödel 5-dimensional charged rotating black holes with two equal angular momenta. It is shown that the spectrum of proper oscillations of the perturbation includes superradiant unstable modes. The reason for the instability is the confining Dirichlet boundary condition at the asymptotically far region of the Gödel Universe. The confining box makes superradiant modes extract rotational energy from the black hole and, after repeated reflections from the black hole, grow unboundedly. A similar instability takes place for rotating black h…
As in the grand canonical treatment of Reissner - Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
Recently, a new interesting instability of a charged scalar field in the Reissner-Nordström-de Sitter background has been found (arXiv:1405.4931v2) through the time-domain integration of the perturbation equation. We investigate further properties of this instability, confirm its existence by concordant frequency-domain and time-domain calculations and show that it occurs at however small value of the coupling eQ, where e and Q are charges of a scalar field and black hole respectively. We also investigate the parametric region of instability and show that the critical values of eQ at which the…
We investigate instability of 4-dimensional Reissner-Nordström-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of…
We investigate the stability of a free scalar field nonminimally coupled to gravity under linear perturbations in the spacetime of a charged spherical shell. Our analysis is performed in the context of quantum field theory in curved spacetimes. This paper completes previous analyses which considered the exponential enhancement of vacuum fluctuations in the spacetime of massive shells.
We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality t…
We analyze in detail the quantum instability which characterizes charged scalar field on three special de Sitter charged black hole backgrounds. In particular, we compute exactly the imaginary part of the effective action for scalar charged fields on the ultracold I, ultracold II and Nariai charged black hole backgrounds. Both the transmission coefficient approach and the $ζ$-function approach are exploited. Thermal effects on this quantum instability are also taken into account in presence of a non-zero black hole temperature (ultracold I and Nariai).
We study the thermodynamics in the grand canonical ensemble of D-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range $0<Φ<\frac{\sqrt{3}π}{4}$. For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom-AdS black holes, with …
We study the linear instability of the charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet-AdS black holes by exploring the quasinormal modes. We find that the linear instability is triggered by superradiance. The charged massless scalar perturbation becomes more unstable when increasing the Gauss-Bonnet coupling constant or the black hole charge. Meanwhile, decreasing} the AdS radius will make the charged massless scalar perturbation} more stable. The stable region in parameter space $(α,Q,Λ)$ is given. Moreover, we find that the charged massless scalar pertur…
We find a new instability in the four-dimensional Reissner-Nordstrom-de Sitter black holes against charged scalar perturbations with vanishing angular momentum, $l=0$. We show that such an instability is caused by superradiance. The instability does not occur for an larger angular index, as explicitely proven for $l=1$. Our results are obtained from a numerical investigation of the time domain profiles of the perturbations.
We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius…
Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter $n$. It is also shown that the solutions presented h…
We study the stabilities of (A)dS charged Gauss-Bonnet(GB) black holes in the large $D$ dimensions. After integrating the equation of motion with respect to the radial direction, we obtain the effective equations at large $D$ to describe the nonlinear dynamical deformations of the black hole. From the perturbation analysis of the effective equations, we get the analytic expressions of the frequencies for the quasinormal modes of scalar type. Furthermore we show that the charged GB black hole becomes unstable only if the cosmological constant is positive, otherwise the black hole is always stab…
Black holes possess trapping regions which lead to intriguing dynamical effects. By properly scattering test fields off a black hole, one can extract energy from it, leading to the growth of the amplitude of the test field in expense of the black hole's energy. Such a dynamical phenomenon is called superradiance. Here, we study charged-scalar-field instabilities of Reissner-Nordström black holes immersed in a $d-$dimensional de Sitter Universe. By performing a thorough frequency-domain analysis we compute the unstable quasinormal resonances and link their presence with a novel family of quasin…
In our earlier work (PRL 103 (2009) 161101) it was shown that nonextremal highly charged Reissner-Nordstrom-de Sitter black holes are gravitationally unstable in D>6-dimensional space-times. Here, we find accurate threshold values of the $Λ$-term at which the instability of the extremally charged black holes starts. The larger $D$ is, the smaller is the threshold value of $Λ$. We have shown that the ratio $ρ= r_{h}/r_{cos}$ (where $r_{cos}$ and $r_{h}$ are the cosmological and event horizons) is proportional to $e^{-(D-4)/2}$ at the onset of instability for D=7,8,...11, implying that the same …
We study the instability of charged anti-de Sitter black holes in four or higher-dimension under fragmentation. The instability of fragmentation breaks the black hole into two black holes. We have found that the region near extremal or massive black holes become unstable under fragmentation. These regions depend not only on the mass and charge of initial black hole but also those of the fragmented one. The instability in higher-dimension is qualitatively similar to that of four-dimension. The detailed instabilities are numerically investigated.
The magnetically charged SU(2) Reissner-Nordström black-hole solutions of the coupled nonlinear Einstein-Yang-Mills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances $\{ω_n(r_+,r_-)\}_{n=0}^{n=\infty}$ (here $r_{\pm}$ are the black-hole horizon radii). Based on direct {\it numerical} computations of the black-hole instability spectra, it has recently been observed that the excited instability eigenvalues of the magnetically charged black holes exhibit a simple universal behavior. In particular, it was shown that the numerically computed instab…
We study the instability of small AdS black holes with two independent rotation parameters in minimal five-dimensional gauged supergravity to massless scalar perturbations. We analytically solve the Klein-Gordon equation for low-frequency perturbations in two regions of the spacetime of these black holes: namely, in the region close to the horizon and in the far-region. By matching the solutions in an intermediate region, we calculate the frequency spectrum of quasinormal modes. We show that in the regime of superradiance only the modes of even orbital quantum number undergo negative damping, …
We have shown that higher dimensional Reissner-Nordström-de Sitter black holes are gravitationally unstable for large values of the electric charge and cosmological constant in $D \geq 7$ space-time dimensions. We have found the shape of the slightly perturbed black hole at the threshold point of instability. Why only $D=4, 5$ and 6 dimensional worlds are favorable as to the black stability remains unknown.
We studied the instability of the regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes under charged scalar perturbations. The unstable modes satisfy the superradiant condition, but not all modes satisfying the superradiant condition are unstable. The instability occurs when the cosmological constant is small and the black hole charge is not too large. The Gauss-Bonnet coupling constant makes the unstable black hole more unstable when both the black hole charge and cosmological constant are small, and makes the stable black hole more stable when the black hole charge is large.
When a scalar wave perturbation is properly scattering off a charged or rotating black hole, the energy of the reflected scalar wave may be amplified. This is a superradiant process. If this amplification process can occur back and forth through certain confining mechanism, it will lead to strong instability of the black hole. In this paper, the superradiant stability is investigated for a special kind of dyonic black holes in string theory. Although the dynoic black hole has a similar spacetime metric with a electrically charged RN black hole, it is found that the dyonic black hole is more un…
In this paper, we discuss dynamical instability of charged dissipative cylinder under radial oscillations. For this purpose, we follow the Eulerian and Lagrangian approaches to evaluate linearized perturbed equation of motion. We formulate perturbed pressure in terms of adiabatic index by applying the conservation of baryon numbers. A variational principle is established to determine characteristic frequencies of oscillation which define stability criteria for gaseous cylinder. We compute the ranges of radii as well as adiabatic index for both charged and uncharged cases in Newtonian and post-…
In this paper, we investigate the thermodynamics of hyperscaling violating Lifshitz black branes in the presence of a nonlinear massless electromagnetic field. We, first, obtain analytic nonlinear charged black brane solutions with hyperscaling violating factor in dilaton gravity and give the condition on the parameters of the metric for having black brane solutions. Second, we introduce the appropriate finite action in grand-canonical and canonical ensembles for nonlinear electromagnetic field. Next, by generalizing the counterterm method for the asymptotic Lifshitz spacetimes with hyperscali…
Similar to the superradiant effect in Reissner-Nordström black hole, a charged scalar field can be amplified when impinging on the charged black hole in string theory. According to the black-hole bomb mechanism,the mass term of the incident field can works as the reflecting mirror, which may trigger the instability of black hole. We study the possible instability triggered by superradiant effect and demonstrate that the charged black hole in string theory is stable against the massive charged scalar perturbation. The reason is that there is no trapping potential well in the black hole exterior…
In this paper we show that electrically charged black holes in Einstein-Gauss-Bonnet gravity suffer from a superradiant instability. It is triggered by a charged scalar field that fulfills Dirichlet boundary conditions at a mirror located outside the horizon. As in General Relativity, the unstable modes exist provided the mirror is located beyond a critical radius, making the instability a long wavelength one. We explore the effects of the Gauss-Bonnet corrections on the critical radius and find evidence that the critical radius decreases as the Gauss-Bonnet coupling $α$ increases. Due to the,…
In this post, a new variable y($μ=yω$) is added to extend the results of the above post. We derive a very compact resonance formulation. When y is a certain limit, the effective potential of the equation exists at the pole, and the potential well appears outside the event horizon, when ${e}^{-4αΦ/(n-1)}\sqrtα Q \ll r_{+}\ll 1 / (\frac{4}{n-1}y) $, so charged dilator black hole is superradiatively unstable at this time.
It has been shown that the mass of the scalar field in the charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against the massive charged scalar perturbation. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the unstable superradiant modes is derived by using the asymptotic matching method. It is also poin…
In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeine…
It is well-known that the SU(2) Reissner-Nordström black-hole solutions of the Einstein-Yang-Mills theory are characterized by an infinite set of unstable (imaginary) eigenvalues $\{ω_n(T_{\text{BH}})\}_{n=0}^{n=\infty}$ (here $T_{\text{BH}}$ is the black-hole temperature). In this paper we analyze the excited instability spectrum of these magnetically charged black holes. The numerical results suggest the existence of a universal behavior for these black-hole excited eigenvalues. In particular, we show that unstable eigenvalues in the regime $ω_n\ll T_{\text{BH}}$ are characterized, to a very…
We study entropy corrections due to thermal fluctuations for asymptotically AdS black holes in the grand canonical ensemble. To leading order, these can be expressed in terms of the black hole response coefficients via fluctuation moments. We also analyze entropy corrections due to mass and charge fluctuations of R-charged black holes, and our results indicate an universality in the logarithmic corrections to charged AdS black hole entropy in various dimensions.
A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent evolution equations of small perturbations are constructed.
In the subject of black hole chemistry, a broad variety of critical phenomena for charged topological black holes (TBHs) with massive gravitons (within the framework of dRGT massive gravity) is discussed in detail. Since critical behavior and nature of possible phase transition(s) crucially depend on the specific choice of ensemble, and, in order to gain more insight into criticality in the massive gravity framework, we perform our analysis in both the canonical (fixed charge, $Q$) and the grand canonical (fixed potential, $Φ$) ensembles. It is shown that, for charged TBHs in the grand canonic…
It has been proved that the charged stringy black holes are stable under the perturbations of massive charged scalar fields. However, superradiant instability can be generated by adding the mirror-like boundary condition to the composed system of charged stringy black hole and scalar field. The unstable boxed quasinormal modes have been calculated by using both analytical and numerical method. In this paper, we further provide a time domain analysis by performing a long time evolution of charged scalar field configuration in the background of the charged stringy black hole with the mirror-like…
The well-known superradiant amplification mechanism allows a charged scalar field of proper mass $μ$ and electric charge $q$ to extract the Coulomb energy of a charged Reissner-Nordström black hole. The rate of energy extraction can grow exponentially in time if the system is placed inside a reflecting cavity which prevents the charged scalar field from escaping to infinity. This composed black-hole-charged-scalar-field-mirror system is known as the {\it charged black-hole bomb}. Previous numerical studies of this composed physical system have shown that, in the linearized regime, the inequali…
In the context of Black Hole Chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics are discussed in the grand canonical (fixed $U(1)$ potential, $Φ$) ensemble. Considering all higher-order graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, exact TBH solutions are derived, the explicit form of the on-shell action is computed, and the associated thermodynamic quantities in the Grand Canonical Ensemble (G…
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass un…
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that …
We investigate the instability of the unstable circular orbit of a charged null particle to test the strong cosmic censorship conjecture in Nariai-type near-extremal Reissner--Nordström--de Sitter black holes. The instability is estimated as the Lyapunov exponent and found to depend on the mass and charge of the black hole. Then, we explicitly show that charged null particles in unstable circular orbits correspond to the charged massless scalar field in the eikonal limit. This provides a compact relationship representing the quasinormal frequency in terms of the characteristics of unstable cir…
Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical system of scalar-charged degenerate fermions, a numerical model of the cosmological evolution of gravitational-scalar perturbations is constructed and specific examples of the development of instability are given. Some features of the instability's development are investigated depending on the nature of the behavior of the unperturbed cosmological model. It is shown that …
We study the thermodynamic properties of the RN-AdS black hole in full phase space and propose a generalized thermodynamic identity. As an example, we use it to find relations of thermodynamical coefficients between the grand canonical and canonical ensembles. We also show, for the first order phase transition, that the usual Maxwell's equal area law should be extended to a new form for the RN-AdS black hole.
We provide evidence that ``super-extremal'' black hole space-times (either with charge larger than mass or angular momentum larger than mass), which contain naked singularities, are unstable under linearized perturbations. This is given by an infinite family of exact unstable solutions in the charged non rotating case, and by a set of (unstable) numerical solutions in the rotating case. These results may be relevant to the expectation that these space-times cannot be the endpoint of physical gravitational collapse.
We consider the thermodynamics of a charged black hole enclosed in a cavity. The charge in the cavity and the temperature at the walls are fixed so that we have a canonical ensemble. We derive the phase structure and stability of black hole equilibrium states. We compare our results to that of other work which uses asymptotically anti-de Sitter boundary conditions to define the thermodynamics. The thermodynamic properties have extensive similarities which suggest that the idea of AdS holography is more dependent on the existence of the boundary than on the exact details of asymptotically AdS m…
We present here how the gravothermal or Antonov's instability, which was originally formulated in the microcanonical ensemble, is modified in the presence of a cosmological constant and in the canonical ensemble. In contrast to the microcanonical ensemble, there is a minimum, and not maximum, radius for which metastable states exist. In addition this critical radius is decreasing, and not increasing, with increasing cosmological constant. The minimum temperature for which metastable states exist is decreasing with increasing cosmological constant, while above some positive value of the cosmolo…
We obtain a charged accelerating AdS black hole solution in $f(R)$ gravity and investigate its thermodynamic behaviour. We consider low-acceleration black holes that do not have an acceleration horizon and obtain the first law of thermodynamics for them. We further study the parameter space of charged slowly accelerating $f(R)$ AdS black holes before investigating the behaviour of the free energy in both the canonical and grand canonical ensembles. We find a generalization of the reverse isoperimetric inequality, applicable to black holes in $f(R)$ gravity, that indicates these black holes can…
In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ru…
We investigate the quasibound states of charged massive scalar fields in the Kerr-Newman black hole spacetime by using a new approach recently developed, which uses the polynomial conditions of the Heun functions. We calculate the resonant frequencies related to the spectrum of quasibound states, as well as its corresponding angular and radial wave eigenfunctions. We also analyze the instability of the system. These results are particularized to the cases of Schwarzschild and Kerr black holes. Additionally, we compare our analytical results with the numerical ones known in the literature. Fina…
