We study the Schwinger effect in near-extremal nonrotating black holes in an arbitrary $D(\geq 4)$-dimensional asymptotically flat and (A)dS space. Using the near-horizon geometry $\mathrm{AdS}_2 \times \mathrm{S}^{D-2}$ of near-extremal black holes with Myers-Perry metric, we find a universal expression of the emission formula for charges that is a multiplication of the Schwinger effects in an $\mathrm{AdS}_2$ space and in a two-dimensional Rindler space. The effective temperature of an accelerated charge for the Schwinger effect is determined by the radii of the effective $\mathrm{AdS}_2$ space and $\mathrm{S}^{D-2}$ as well as the mass, charge, angular momentum of the charge and the radius of the (A)dS space. The Schwinger effect in the asymptotically flat space is more efficient and persistent for a wide range of large black holes for dimensions higher than four. The AdS (dS) boundary enhances (suppresses) the Schwinger effect than the asymptotically flat space. The Schwinger effect persists for a wide range of black holes in the AdS space and has an upper bound in the dS space.
We propose a thermal interpretation of the Schwinger effect for charged scalars and spinors in an extremal and near-extremal Reissner-Nordström (RN) black hole. The emission of charges has the distribution with an effective temperature determined by the Davies-Unruh temperature for accelerating charges by the electric field and the scalar curvature of AdS_2 from the near-horizon geometry AdS_2 X S^2. We find a charge bound for the extremal micro black hole to remain stable against the Schwinger emission in analogy with the Breitenlohlner-Freedman bound for the AdS space. In the in-out formalis…
We study the Schwinger effect in near-extremal Reissner-Nordström (RN) black holes with electric and/or magnetic charges in the (Anti-) de Sitter (AdS) space. The formula for the Schwinger effect takes a universal form for near-extremal black holes with the near-horizon geometry of ${\rm AdS}_2 \times S^2$ and with the proper radii for the ${\rm AdS}_2$ space and the two-sphere $S^2$, regardless of the asymptotically flat or (A)dS space. The asymptotic AdS boundary enhances and the dS boundary suppresses the Schwinger effect and the small radius of the AdS (dS) space reinforces the enhancement…
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…
Using the symmetry of the near-horizon geometry and applying quantum field theory of a complex scalar field, we study the spontaneous pair production of charged scalars from near-extremal rotating, electrically and/or magnetically charged black holes. Analytical expressions for pair production, vacuum persistence and absorption cross section are found, and the spectral distribution is given a thermal interpretation. The pair production in near-extremal black holes has a factorization into the Schwinger effect in AdS and Schwinger effect in Rindler space, measuring the deviational from extremal…
The spontaneous pair production of charged scalars in a near extremal Kerr-Newman (KN) black hole is analytically studied. It is shown that the existence condition for the pair production is equivalent to the violation of the Breitenlohner-Freedman bound in an AdS$_2$ space. The mean number of produced pairs in the extremal black hole has a thermal interpretation, in which the effective temperature for the Schwinger effect in the AdS$_2$ space persistently holds, while the mean number in the near extremal black hole has an additional factor of the Schwinger effect in the Rindler space. In addi…
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.
Using the enhanced symmetry in the near-horizon region of the near-extremal dyonic Kerr-Newman (KN) black hole in the (A)dS space, we find the exact solutions for dyonic charged scalar field in terms of the hypergeometric function and explicitly compute the Schwinger effect for the emission of electric and/or magnetic charges. The emission formula confirms a universal factorization of the Schwinger formula in the AdS$_2$ and another Schwinger formula in the two-dimensional Rindler space determined by the effective temperature and the Hawking temperature with the chemical potentials of electric…
Recent researches of the novel $4D$ Einstein-Gauss-Bonnet (EGB) gravity have attracted great attention. In this paper, we investigate the validity of the weak cosmic censorship conjecture for a novel $4D$ charged EGB black hole with test charged scalar field and test charged particle respectively. For the test charged field scattering process, we find that both extremal and near-extremal black holes cannot be overcharged. For the test charged particle injection, to first order, an extremal black hole cannot be overcharged while a near-extremal $4D$ charged EGB black hole can be destroyed. To s…
We present a unified picture for the Schwinger effect and the Hawking radiation and address the gauge-gravity relation and the dS-AdS duality issue at the one-loop level. We propose a thermal interpretation for the Schwinger effect in an (A)dS space and in an Reissner-Nordström black hole. The emission of charged particles from the near-extremal charged black hole is proportional to the Schwinger effect in an AdS and to another Schwinger effect in a Rindler space accelerated by the surface gravity.
We revisit the Schwinger effect in de Sitter, anti-de Sitter spaces and charged black holes, and explore the interplay between quantum electrodynamics and the quantum gravity effect at one-loop level. We then advance a thermal interpretation of the Schwinger effect in curved spacetimes. Finally, we show that the Schwinger effect in a near-extremal black hole differs from Hawking radiation of charged particles in a non-extremal black hole and is factorized into those in an anti-de Sitter space and a Rindler space with the surface gravity for acceleration.
We construct the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case with only one rotation parameter and two independent charges. Using the Boyer-Lindquist coordinates, the metric is expressed in a generalized form of the ansatz previously presented in [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], which may be helpful to find the most general non-extremal two-charged rotating black hole with three unequal rotation parameters. The conserved charges for thermodynamics are also computed.
We study the spontaneous pair production, including the Schwinger mechanism and the Hawking radiation, of charged scalar and spinor particles from the near horizon region of (near) extremal charged black holes in the probe field limit. The pair production rate and the absorption cross section, as well as the retarded Green's functions of the probe fields are analytically computed. Moreover, the holographic description dual to the pair production is discussed.
In an (Anti-) de Sitter space and a charged black hole the Schwinger effect is either enhanced by the Hawking radiation or suppressed by the negative curvature. We use the contour integral method to calculate the production of charged pairs in the global (A)dS space. The charge emission from near-extremal black hole is found from the AdS geometry near the horizon and interpreted as the Schwinger effect in a Rindler space with the surface gravity for the acceleration as well as the Schwinger effect in AdS space.
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.
It is shown that the charged massive Schwinger model supports a periodic vacuum structure for arbitrary charge density, similar to the common crystalline layout known in solid state physics. The dynamical origin of the inhomogeneity is identified in the framework of the bozonized model and in terms of the original fermionic variables.
It was recently shown that the extremal charged black holes in STU supergravity suffer from superradiant instability owing to the existence of the unstable (low-frequency) quasibound states associated with a charged massive scalar field. In this paper, we show numerically that for some charge configurations, these black holes can also excite the (higher-frequency) superradiantly unstable quasinormal modes. We find empirically that the unstable modes are closely related to having a volcano-shaped effective potential in the Schrödinger-like wave equation.
We construct asymptotically Kaluza-Klein solutions in five-dimensional Einstein-Maxwell theory which represent a pair of extremal, charged, static black holes on Kerr-Taub-bolt space. Regularity conditions require that the topology of spatial infinity and that of each black hole are not S$^3$, but different lens spaces. We show that for a given topology at spatial infinity, there are an infinite number of different horizon topologies for the black hole pair. We briefly discuss a generalization to the case with a positive cosmological constant.
In quantum field theory, particle creation occurs, in general, when an intense external field, such as an electromagnetic field, breaks time translational invariance. This leads to an ambiguity in the definition of the vacuum state. In cosmological backgrounds this ambiguity has been reduced by imposing that the quantization preserves the symmetries of the system and that the dynamics is unitarily implemented. In this work, we apply these requirements to the quantization of a massive charged fermionic field coupled to a classical time-dependent homogeneous electric field, extending previous st…
In the presence of a dilatonic coupling between an inflaton and a $U(1)$ gauge field, a persistent electric field (i.e., an anisotropic inflation) is obtained as a solution of the classical field equations. We introduce charged, massive, and conformally coupled fields into this model and study the pair production of charged particles. The semiclassical approach allows us to evaluate the induced current due to the pair production on the general dilatonic factor and electric field. Solving the field equations with the induced current, we find that the electric field shows a damped oscillation, w…
We study the properties of the Green's functions of the fermions in the extremal charged dilatonic black hole proposed by Gubser and Rocha [Phys. Rev. D \textbf{81}, 046001 (2010)]. We find that many properties seem to be in agreement with that of Fermi liquid. Especially, the dispersion relation is linear. It is very different from that found in the extremal Reissner-Nordstr$\ddot{o}$m (RN) black hole for massless fermion, which is obviously non-Fermi liquid due to a nonlinear dispersion relation. However, for another scaling behavior of the height of $ImG_{11}$ at the maximum, the scaling ex…
We consider charged black holes within dilaton gravity with exponential-linear dependence of action coefficients on dilaton and minimal coupling to quantum scalar fields. This includes, in particular, CGHS and RST black holes in the uncharged limit. For non-extremal configuration quantum correction to the total mass, Hawking temperature, electric potential and metric are found explicitly and shown to obey the first generalized law. We also demonstrate that quantum-corrected extremal black holes in these theories do exist and correspond to the classically forbidden region of parameters in the s…
We study static, spherically symmetric and electrically charged black hole solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very similar to the uncharged case, black holes undergo spontaneous scalarization for sufficiently large scalar-tensor coupling $γ$ - a phenomenon attributed to a tachyonic instability of the scalar field system. While in the uncharged case, this effect is only possible for positive values of $γ$, we show that for sufficiently large values of the electric charge $Q$ two independent domains of existence in the $γ$-$Q$-plane appear: one for positive $γ$ …
We have shown that changes occur in a (2+1)-dimensional charged black hole by adding a charged probe. The particle increases the entropy of the black hole and guarantees the second law of thermodynamics. The first law of thermodynamics is derived from the change in the black hole mass. Using the particle absorption, we test the extremal black hole and find out that the mass of the extremal black hole increases more than the electric charge. Therefore, the outer horizon of the black hole still exists. However, the extremal condition becomes non-extremal.
In this paper, inspired by the holographic dual of the entanglement entropy, we consider the behaviour of extremal, codimension two, spacelike surfaces in the background of three and four dimensional charged boson stars in asymptotically anti-de Sitter spacetime. We find conditions for which families of minimal area surfaces fail to contain the entire bulk spacetime and construct a phase diagram showcasing the transition between regimes. In addition, we use the relation between the star's mass and the central density of the scalar field to argue for a possible instability of such hollow soluti…
The destruction of a regular black hole event horizon might provide us the possibility to access regions inside black hole event horizon. This paper investigates the possibility of overcharging a charged Taub-NUT regular black hole via the scattering of a charged field and the absorption of a charged particle. For the charged scalar field scattering, both the near-extremal and extremal charged Taub-NUT regular black holes cannot be overcharged. For the test charged particle absorption, the result shows that the event horizon of the extremal charged Taub-NUT regular black hole still exists whil…
We construct odd-dimensional extremal charged black hole solutions with a twisted S^1 as an extra dimension on generalized Euclidean Taub-NUT spaces. There exists a null hypersurface where an expansion for an outgoing null geodesic congruence vanishes, then these spacetimes look like black holes. We show that the metrics admit C^0 extension across the horizon, but some components of Riemann curvature diverge there if the dimension is higher than five. The singularity is not much strong so that an observer along a free-fall geodesic can traverse the horizon. We also show solutions with a positi…
We analyze the late-time decay of scalar perturbations in extremal Reissner-Nordstrom spacetime. We consider individual spherical-harmonic modes $l$ of a test massless scalar field, restricting our attention to initial data of compact support, with generic regular behavior across the horizon. We obtain a decay rate $\propto t^{-(2l+3)}$ (just like in Schwarzschild) for incident waves scattered by the black hole. However, for waves originating at the horizon's neighborhood we obtain a slightly slower decay, $\propto t^{-(2l+2)}$. We discuss relations to previous works.
We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.
We find solution to the metric function f(r)=0 of charged BTZ black hole making use of the Lambert function. The condition of extremal charged BTZ black hole is determined by a non-linear relation of M_e(Q)=Q^2(1-\ln Q^2). Then, we study the entropy of extremal charged BTZ black hole using the entropy function approach. It is shown that this formalism works with a proper normalization of charge Q for charged BTZ black hole because AdS_2 x S^1 represents near-horizon geometry of the extremal charged BTZ black hole. Finally, we introduce the Wald's Noether formalism to reproduce the entropy of t…
Extremal rotating black holes in Einstein-Maxwell theory feature two branches. On the branch emerging from the Myers-Perry solutions their angular momentum is proportional to their horizon area, while on the branch emerging from the Tangherlini solutions their angular momentum is proportional to their horizon angular momentum. The transition between these branches occurs at a critical value of the charge, which depends on the value of the angular momentum. However, when a dilaton is included, the angular momentum is always proportional to the horizon area.
Pair-production of magnetic Reissner-Nordström black holes (of charges $\pm q$) was recently studied in the leading WKB approximation. Here, we consider generic quantum fluctuations in the corresponding instanton geometry given by the Euclidean Ernst metric, in order to simulate the behaviour of the one-loop tunneling rate. A detailed study of the Ernst metric suggests that for sufficiently weak field $B$, the problem can be reduced to that of quantum fluctuations around a single near-extremal Euclidean black hole in thermal equilibrium with a heat bath of finite size. After appropriate renorm…
We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace the origin of the inconsistency between a charge and rotation, considering the BR-like spacetime as a result of the limiting transition of a non-extremal black hole to the extremal state. We also find that the quasilocal energy and angular momentum of such BR-like spacetimes calculated within the boundary $l=const$ ($l$ is the proper distance) are constants …
We recover the properties of a wide class of far from extremal charged black branes from the properties of near extremal black branes, generalizing the results of Danielsson, Guijosa and Kruczenski.
We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume. The variation exactly corresponds to that expected as the first law of thermodynamics. Nevertheless, we find the decrease of the Bekenstein-Hawking entropy for extremal and near-extremal black holes under the absorption to be an irreversible process. This violation of the second law of thermodynamics is only found in the case considering thermodynamic volume. We test the weak cosmic censorship conjecture affected by the violation. Fortunately, the conject…
Employing higher order perturbation theory, we obtain charged rotating black holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter, and focus on extremal black holes with equal-magnitude angular momenta. For Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling constant, we perform the perturbations up to third order for any odd dimension. We discuss the physical properties of these black holes and study their dependence on…
QED in 1+1 dimensions possesses two rare and interesting properties - It is both exactly solvable and confining. The combination of these two properties makes it the perfect candidate for a toy model for QCD. We study this model on an interval, where new features of the theory are revealed. We show that on an interval, the model admits charged states, which is unexpected for a confining theory. We show that the charged states are boundary states, and calculate their mass. This result could lead one to expect a similar result in QCD, where single quarks could be isolated near a boundary.
We investigate the spontaneous pair production, including the Schwinger mechanism and the Hawking thermal radiation, of charged scalar particles from the near horizon region of a (near) extremal Reissner-Nordström black hole. The paradigm is equivalent to the dynamics of the charged scalar field in a specific AdS$_2 \times S^2$ spacetime with a constant electric field. Two possible boundary conditions are adopted to explicitly compute the corresponding production rate and absorption cross section. It is shown that the Schwinger production rate can be eventually suppressed by the increasing att…
Using a unified approach we study the entropy of extremal black holes through the entropy of an electrically charged thin shell. We encounter three cases in which a shell can be taken to its own gravitational or horizon radius and become an extremal spacetime. In case 1, we use a non extremal shell, calculate all the thermodynamics quantities including the entropy, take it to the horizon radius, and then take the extremal limit. In case 2, we take the extremal limit and the horizon radius limit simultaneously, i.e., as the shell approaches its horizon radius it also approaches extremality. In …
In this paper we employ the results of a previous paper on the late-time decay of scalar-field perturbations of an extreme Reissner-Nordstrom black hole, in order to find the late-time decay of coupled electromagnetic and gravitational perturbations of this black hole. We explicitly write the late-time tails of Moncrief's gauge invariant variables and of the perturbations of the metric tensor and the electromagnetic field tensor in the Regge-Wheeler gauge. We discuss some of the consequences of the results and relations to previous works.
Logarithmic corrections to near-extremal entropy of charged de Sitter black holes
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Pohang University of Science and Technology (POSTECH)（韩国科学技术院）；Asia Pacific Center for Theoretical Physics, POSTECH（韩国科学技术院亚太理论物理中心）；Seoul National University（首尔国立大学）
The quasinormal resonance spectrum $\{ω_n(μ,q,M,Q)\}_{n=0}^{n=\infty}$ of charged massive scalar fields in the charged Reissner-Nordström black-hole spacetime is studied {\it analytically} in the large-coupling regime $qQ\gg Mμ$ (here $\{μ, q\}$ are respectively the mass and charge coupling constant of the field, and $\{M,Q\}$ are respectively the mass and electric charge of the black hole). This physical system provides a striking illustration for the validity of the universal relaxation bound $τ\times T \geq \hbar/π$ in black-hole physics (here $τ\equiv 1/\Imω_0$ is the characteristic relaxa…
We reconsider over-charging the higher-dimensional nearly extremal charged black holes using the new version of gedanken experiment proposed recently by Sorce and Wald. As a result, we find that cosmic censorship conjecture associated with such black holes is restored by taking into account the second-order correction, albeit violated by the first-order perturbation. Namely, the higher-dimensional nearly extremal charged black holes cannot be over-charged.
We investigate the weak cosmic censorship conjecture in charged anti-de Sitter black holes with thermodynamic pressure and volume by the scattering of the charged scalar field in four and higher dimensions. We assume that the internal energy and electric charge of the black hole changes infinitesimally according to the energy and charge fluxes of the scalar field. Then, found to be an isobaric process, the changes in the black hole can be well reproduced to the first law of thermodynamics, although we find that the second law of thermodynamics is violated in extremal and near-extremal black ho…
The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner-Nordström black-hole spacetime are studied {\it analytically}. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein-Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum…
We test whether static charged dilaton black holes in 2+1 dimensions can be turned into naked singularities, by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also imply that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Baunados-Teitelboim-Zanelli, Kerr and Reissner-Nordström black holes which are overspun or overcharged by a discrete jump. Thus the weak form of the cosmic censorship conjecture and the third la…
The AdS_2\timesS^2 geometry of near-extremal Reissner-Nordstrom black holes can be described by an effective solvable model which allows to follow analytically the evaporation process including the backreaction. We find that an infinite amount of time is required for the black hole to decay to extremality.
Despite recent progress, the complete understanding of the perturbations of charged, rotating black holes as described by the Kerr-Newman metric remains an open and fundamental problem in relativity. In this study, we explore the existence of families of quasinormal modes of Kerr-Newman black holes whose decay rates limit to zero at extremality, called zero-damped modes in past studies. We review the nearly extremal and WKB approximation methods for spin-weighted scalar fields (governed by the Dudley-Finley equation) and give an accounting of the regimes where scalar zero-damped and damped mod…
We compute holographic complexity of charged black brane solutions in arbitrary dimensions for the near horizon limit of near extremal case using two different methods. The corresponding complexity may be obtained either by taking the limit from the complexity of the charged black brane, or by computing the complexity for near horizon limit of near extremal solution. One observes that these results coincide if one assumes to have a cutoff behind horizon whose value is fixed by UV cutoff and also taking into account a proper counterterm evaluated on this cutoff. We also consider the situation f…
We rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately…
