Reissner Nordstrom Anti-de Sitter Research Articles

The Generalised Reissner–Nordstrom Spacetimes, the Cosmological Constant and the Linear Term

The Reissner–Nordstrom spacetimes and some generalised Reissner–Nordstrom spacetimes are analysed. The blackhole solutions are considered. The generalised Reissner–Nordstrom spacetimes with a cosmological-constant term, endowed with a Schwarzschild solid-angle element, are analytically delineated: the radii of the blackholes are analytically calculated and newly parameterised; the coordinate-singularity-avoiding coordinate extension is newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the new conditions for merging the solutions as the physical horizons are analytically outlined; the new parameter space of the model is set and constrained; the new role of the cosmological-constant term in designating the Schwarzschild radius is demonstrated; the Reissner–Nordstrom–deSitter case and in the Reissner–Nordstrom–anti-deSitter one are newly demonstrated to be characterised in a different analytical manner. Furthermore, a new family of solutions is found, qualified after the cosmological-constant term. The generalised Reissner–Nordstrom spacetimes with a linear term, endowed with a Schwarzschild solid-angle element, are analytically studied: the radii are enumerated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are set; the new parameter space of the system is arranged and constrained; the role of the linear-term parameter in the delineation of the Schwarzschild radius is newly proven to be apt to imply a small modification only. The generalised Reissner–Nordstrom spacetimes, endowed with a Schwarzschild solid-angle element, with a linear term and a cosmological-constant term are newly inspected: the radii are analytically calculated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are prescribed; the new parameter space of the scheme is appointed and constrained; the roles of the parameters are newly scrutinised in their application to modify the physical interpretation of the Reissner–Nordstrom parameters only in a small manner; the coordinate-singularity-avoiding coordinate extensions are newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the definition of the physical radii is newly found; the results are newly demonstrated in both cases of a positive value of the cosmological constant and in the case of a negative value of the cosmological constant in a different manner; the role of the linear-term parameter is also newly enunciated. More over, a new family of solutions is found, which is delineated after particular values of the linear term and of the cosmological-constant one. The quantum implementation of the models is prospectively envisaged.

Circular motion of charged particles near a charged black hole

We study the circular motion of charged particles near a charged black hole. The general form of the Lyapunov exponent of charged particles is obtained by using the Jacobian matrix. The results show that the chaos bound can be saturated by the circular motion of charged particles on the horizon. By further expanding the Lyapunov exponent near the horizon and investigating Reissner-Nordstr\"om(RN) black holes with different $M/Q$, we find that in contrast to the static equilibrium, the circular motion of charged particles can have a larger Lyapunov exponent due to the existence of angular momentum. For the RN black holes which have the mass-charge ratio $1<M/Q <1.1547$, the chaos bound is locally violated by the null and the time-like circular motion with large angular momentum. As an illustration of the universality of our results, we study the charged particles' circular motion near the Reissner-Nordstr\"om Anti-de Sitter (RN-AdS) black hole and find that the null and the time-like circular motion with large angular momentum can exceed the chaos bound under the background of RN-AdS black holes with the mass-charge ratio in the range $1.23132<M/Q<1.75225$.

Dynamical charged black hole spontaneous scalarization in anti–de Sitter spacetimes

We study the fully nonlinear dynamics of the spherically symmetric black hole spontaneous scalarization in Einstein Maxwell scalar theory with coupling function $f(\ensuremath{\phi})={e}^{\ensuremath{-}b{\ensuremath{\phi}}^{2}}$, which can transform usual Reissner-Nordstr\"om anti--de Sitter (RN-AdS) black holes into hairy black holes. Fixing the Arnowitt-Deser-Misner mass of the system, the initial scalar perturbation will destroy the original RN-AdS black hole and turn it into a spherically symmetric hairy black hole provided that the constant $\ensuremath{-}b$ in the coupling function and the charge of the original black hole are sufficiently large, while the cosmological constant is small enough. In the scalarization process, we observe that the black hole irreducible mass initially increases exponentially, then it approaches to and finally saturates at a finite value. Choosing stronger coupling and larger black hole charge, we find that the black hole mass exponentially grows earlier and it takes longer time for a hairy black hole to be developed and stabilized. We further examine phase structure properties in the scalarization process and confirm the observations in the nonlinear dynamical study.

Holographic informational properties for a specific Einstein-Maxwell-dilaton gravity theory

We study the holographic information quantities, including the holographic entanglement entropy (HEE), the holographic mutual information (HMI) and the minimum cross section of the entanglement wedge (EWCS), over a special black brane geometry, which has a vanishing ground-state entropy. Thanks to the zero entropy density at the ground state, we expect to extract novel, even singular informational properties in the zero-temperature limit. Surprisingly, we do not observe any singular behavior of entanglement-related physical quantities in the zero-temperature limit. Nevertheless, we find a peculiar property from this model that in the low-temperature region, the HEE decreases with the temperature, which is contrary to that in most holographic models. We argue that this novel phenomenon is brought by the singular property of the zero-temperature limit. In addition, we also compare the features of the information quantities in this special black brane geometry with those in Reissner-Nordstrom anti--de Sitter (RN-AdS) black brane geometry. It is shown that the HEE and HMI of this vanishing ground-state entropy model are always larger than those of RN-AdS geometry, while the EWCS behaves oppositely. Our results indicate that the HMI and EWCS could have different abilities in describing mixed state entanglement.

Charged Dirac perturbations on Reissner-Nordström–anti–de Sitter spacetimes: Quasinormal modes with Robin boundary conditions

We study charged Dirac quasinormal modes (QNMs) on Reissner-Nordstr\"om-Anti-de Sitter (RN-AdS) black holes with generic Robin boundary conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin boundary conditions compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the quasinormal spectrum for charged Dirac fields, and analyse the impact of various parameters, in particular of electric charge. An analytic calculation shows explicitly that the charge coupling between the black hole and the Dirac field does not trigger superradiant instabilities. Numeric calculations, on the other hand, show quantiatively that Dirac QNMs may change substantially due to the electric charge. Our results illustrate how vanishing energy flux boundary conditions, as a generic principle, are applicable not only to neutral but also to electrically charged fields.

Extended Phase Space in the Framework of Holography**Supported by Iranian National Science Foundation (INSF)

We consider a holographic extended phase space in the presence of Reissner-Nordstrom-Anti-de Sitter (RN-AdS) and Born-Infeld-Anti-de Sitter (BI-AdS) black holes in the bulk. In this extended phase space the cosmological constant is investigated as pressure and volume is defined as the codimension one-time slice in the bulk geometry enclosed by the minimal area appearing in the computation of the holographic entanglement entropy. These thermodynamics quantities can serve as probes of the underlying phase transition dictated by black hole thermodynamics, but do not describe different structures. We find that the isocharges on the pressure-volume plane exhibit a Van der Waals-like structure, for RN-AdS black holes in the background. For BI-AdS black holes, we observe the analogy with a Van der Waals liquid-gas system for βQ > 1/2 and Reentrant phase transition for βQ < 1/2 in the holographic extended phase space. The same holographic thermodynamic behavior is observed when we use the fidelity susceptibility as the volume and the cosmological constant as the pressure for RN-AdS black hole in the background.

Superradiance and dynamical evolution of a charged scalar field in an asymptotically anti–de-Sitter dilatonic black hole

We study the dynamics of charged massless scalar fields in asymptotically anti–de Sitter (AdS) dilatonic black holes. The instability of the scalar field, which is triggered by the charged superradiant effect and Dirichlet boundary condition at AdS spatial infinity, can be notably described by exponential growth of the scalar field amplitude in time evolving and unstable quasinormal modes of scalar field perturbation. The numerical computation to demonstrate the superradiant instability of the charged scalar field are performed in the time domain and frequency domain, respectively. We confirm the mode that dominates long time behavior of scalar field matches with quasinormal mode obtained from frequency domain analysis quite well. It is well known the small Reissner-Nordstrom-anti–de Sitter (RN-AdS) black holes are superradiant unstable, while the large RN-AdS black holes are stable against the charged scalar perturbations. According to our numerical results, it is observed that the large dilatonic AdS black holes are also superradiant unstable. At last, we conclude that there exist rapid exponential growing superradiant modes in charged dilatonic AdS black holes, which is significant for the nonlinear dynamical evolution of charged superradiant instability.

Perfect Fluid Dark Matter Influence on Thermodynamics and Phase Transition for a Reissner-Nordstrom-Anti-de Sitter Black Hole

Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square Q2 and the conjugate quantity ψ, where ψ is a function of horizon radius. The first law of thermodynamics and the equation of state are derived in the form Q2=Q2(T,ψ). By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system and can be explained by mean field theory. We also explore the Ruppeiner thermodynamic geometry feature and their connection with microscopic structure. We find that in extended phase space there are existence singularity points of Ruppeiner curvature and they could explained as phase transitions.

Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson Effect

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordstr\"om anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as $p_q=\omega\rho_q$ in which $-1<\omega<-\frac{1}{3}.$ Our calculations are restricted to ansatz: $\omega=-1$ (the cosmological constant regime) and $\omega=-\frac{2}{3}$ (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature $T_i$ of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure $P_i.$ Position of the inverse point $\{T_i,P_i\}$ is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point verse different numerical values of the mass $M$ and the charge $Q$ of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for $M>Q$ in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point $\{T_i,P_i\}$ position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge $Q$. In other words the quintessence dark energy dose not affects on position of the inverse point when the AdS RN black hole takes on small charges.

The modified first laws of thermodynamics of anti-de Sitter and de Sitter space–times

We modify the first laws of thermodynamics of a Reissner–Nordstrom anti-de Sitter black hole and a pure de Sitter space–time by the surface tensions. The corresponding Smarr relations are obeyed. The cosmological constants are first treated as fixed constants, and then as variables associated to the pressures. For the black hole, the law is written as δE=TδS−σδA when the cosmological constant is fixed, where E is the Misner–Sharp mass and σ is the surface tension. Adopting the varied constant, we modify the law as δE0=TδS−σeffδA+VδP, where E0=M−Q22r+ is the enthalpy. The thermodynamical properties are investigated. For the de Sitter space–time, the expressions of the modified laws are different from these of the black hole. The differential way to derive the law is discussed.

Time evolutions of scalar field perturbations in D-dimensional Reissner–Nordström Anti-de Sitter black holes

Reissner-Nordstr\"om Anti-de Sitter (RNAdS) black holes are unstable against the charged scalar field perturbations due to the well-known superradiance phenomenon. We present the time domain analysis of charged scalar field perturbations in the RNAdS black hole background in general dimensions. We show that the instabilities of charged scalar field can be explicitly illustrated from the time profiles of evolving scalar field. By using the Prony method to fit the time evolution data, we confirm the mode that dominates the long time behavior of scalar field is in accordance with the quasinormal mode from the frequency domain analysis. The superradiance origin of the instability can also be demonstrated by comparing the real part of the dominant mode with the superradiant condition of charged scalar field. It is shown that all the unstable modes are superradiant, which is consistent with the analytical result in the frequency domain analysis. Furthermore, we also confirm there exists the rapid exponential growing modes in the RNAdS case, which makes the RNAdS black hole a good test ground to investigate the nonlinear evolution of superradiant instability.

An equal area law for holographic entanglement entropy of the AdS-RN black hole

The Anti-de Sitter-Reissner-Nordstrom (AdS-RN) black hole in the canonical ensemble undergoes a phase transition similar to the liquid-gas phase transition, i.e. the isocharges on the entropy-temperature plane develop an unstable branch when the charge is smaller than a critical value. It was later discovered that the isocharges on the entanglement entropy-temperature plane also exhibit the same van der Waals-like structure, for spherical entangling regions. In this paper, we present numerical results which sharpen this similarity between entanglement entropy and black hole entropy, by showing that both of these entropies obey Maxwell's equal area law to an accuracy of around 1 %. Moreover, we checked this for a wide range of size of the spherical entangling region, and the equal area law holds independently of the size. We also checked the equal area law for AdS-RN in 4 and 5 dimensions, so the conclusion is not specific to a particular dimension. Finally, we repeated the same procedure for a similar, van der Waals-like transition of the dyonic black hole in AdS in a mixed ensemble (fixed electric potential and fixed magnetic charge), and showed that the equal area law is not valid in this case. Thus the equal area law for entanglement entropy seems to be specific to the AdS-RN background.

Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes

We calculate the quasinormal modes of massless scalar perturbations around small and large four-dimensional Reissner-Nordstrom-Anti de Sitter (RN-AdS) black holes. We find a dramatic change in the slopes of quasinormal frequencies in small and large black holes near the critical point where the Van der Waals like thermodynamic phase transition happens. This further supports that the quasinormal mode can be a dynamic probe of the thermodynamic phase transition.

Superradiant instabilities in aD-dimensional small Reissner-Nordström-anti-de Sitter black hole

We investigate the superradiant instability for a charged scalar field in a $D$-dimensional small Reissner--Nordstr\"om--anti-de Sitter (RN-AdS) black hole. First, we solve the charged Klein-Gordon equation analytically by a matching method. We show that the general $D$-dimensional quasinormal frequencies depend on the relation between the angular momentum quantum number, $\ensuremath{\ell}$, and $D$. When $\ensuremath{\ell}$ is a (non-negative) integer multiple of $D\ensuremath{-}3$, i.e. $\ensuremath{\ell}=p(D\ensuremath{-}3)$, we find an analytical quasinormal frequency formula adding a purely imaginary correction to the AdS normal frequencies. This is the case for all $\ensuremath{\ell}$ modes in $D=4$. For general $D$ there are two more cases: i) When $\ensuremath{\ell}$ obeys $\ensuremath{\ell}=(p+\frac{1}{2})(D\ensuremath{-}3)$, which can occur for odd $D$, we observe that the matching method fails, since the near- and far-region solutions have different functional dependences. ii) For all other cases, the analytical quasinormal frequency formula gives a complex correction to the AdS normal frequencies. Second, we perform a numerical calculation which confirms the analytical formulas obtained with the matching method and allows us to explore the case where that method failed. In the latter case, as in the former, we verify that all $\ensuremath{\ell}$ modes for all $D$ may become superradiant, which contradicts a previous claim in the literature.

The Thermodynamical Behaviors of Kerr—Newman AdS Black Holes

We reconsider the study of critical behaviors of Kerr—Newman Anti-de Sitter (AdS) black holes in four dimensions. The study is made in terms of the moduli space parameterized by the charge Q and the rotation parameter a, relating the mass M of the black hole and its angular momentum J via the relation a = J/M. Specifically, we discuss such thermodynamical behaviors in the presence of a positive cosmological constant considered as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. The equation of state for a charged Reissner—Nordstrom AdS black hole predicts a critical universal number depending on the (Q, a) moduli space. In the vanishing limit of the a parameter, this prediction recovers the usual universal number in four dimensions. Then, we find the bounded region of the moduli space allowing the consistency of the model with real thermodynamical variables.

Spectroscopy of the Reissner–Nordström–Anti-de Sitter Black Hole via Adiabatic Invariance

By combining the black hole property of adiabaticity and the oscillating velocity of the black hole horizon, we study the entropy and the area spectra of the Reissner–Nordstrom–anti-de Sitter black hole. Instead of using the quasi-normal mode frequencies, we utilize the oscillating velocity of the event horizon in the tunneling framework to obtain the black hole spectroscopy via adiabatic invariance. The results show that, both of the area spectrum and the entropy spectrum are equally spaced and independent on the parameters of the black hole.

Photons motion in charged Anti-de Sitter black holes

In this work we study the null geodesics in the background of Reissner-Nordstrom Anti de Sitter black hole. We compute the exact trajectories in terms of Weierstrass elliptic functions, obtaining a detailed description of the orbits in terms of the charge, mass and the cosmological constant. The trajectories of the photon are classified using the impact parameter.

Higher-dimensional chargedf(R)black holes

We construct a new class of higher-dimensional black hole solutions of $f(R)$ theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In $n$-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take $n=4p$, where $p$ is the power of conformally invariant Maxwell Lagrangian. These black hole solutions are similar to higher-dimensional Reissner-Nordstrom anti-de Sitter black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher-dimensional $f(R)$ black holes with conformally invariant Maxwell source.

Absence of a Fermi surface in classical minimal four-dimensional gauged supergravity

We demonstrate that the two point function of the supercurrent dual to the gravitino in the four-dimensional extremal anti-de Sitter Reissner-Nordstrom black hole does not exhibit a Fermi surface singularity. In our analysis, we utilize the ingoing Eddington-Finkelstein coordinate system, which enables us to bypass certain complications in the determination of the allowed near horizon behavior of the gravitino field at zero frequency. We check that our method agrees with previous results for the massless charged Dirac field.

Quasinormal modes of a massless charged scalar field on a small Reissner-Nordström-anti-de Sitter black hole

We investigate quasinormal modes of a massless charged scalar field on a small Reissner-Nordstr\"om-anti-de Sitter (RN-AdS) black hole both with analytical and numerical approaches. In the analytical approach, by using the small black hole approximation (r_+ << L), we obtain the quasinormal mode frequencies in the limit of r_+/L -> 0, where r_+ and L stand for the black hole event horizon radius and the AdS scale, respectively. We then show that the small RN-AdS black hole is unstable if its quasinormal modes satisfy the superradiance condition and that the instability condition of the RN-AdS black hole in the limit of r_+/L -> 0 is given by Q>(3/eL)Q_c, where Q, Q_c, and e are the charge of the black hole, the critical (maximum) charge of the black hole, and the charge of the scalar field, respectively. In the numerical approach, we calculate the quasinormal modes for the small RN-AdS black holes with r_+ << L and confirm that the RN-AdS black hole is unstable if its quasinormal modes satisfy the superradiance condition. Our numerical results show that the RN-AdS black holes with r_+ =0.2L, 0.1L, and 0.01L become unstable against scalar perturbations with eL=4 when the charge of the black hole satisfies Q > 0.8Q_c, 0.78Q_c, and 0.76Q_c, respectively.