Reissner-Nordstrom Research Articles

Superluminality, black holes and EFT

Under the assumption that a UV theory does not display superluminal behavior, we ask what constraints on superluminality are satisfied in the effective field theory (EFT). We study two examples of effective theories: quantum electrodynamics (QED) coupled to gravity after the electron is integrated out, and the flat-space galileon. The first is realized in nature, the second is more speculative, but they both exhibit apparent superluminality around non-trivial backgrounds. In the QED case, we attempt, and fail, to find backgrounds for which the superluminal signal advance can be made larger than the putative resolving power of the EFT. In contrast, in the galileon case it is easy to find such backgrounds, indicating that if the UV completion of the galileon is (sub)luminal, quantum corrections must become important at distance scales of order the Vainshtein radius of the background configuration, much larger than the naive EFT strong coupling distance scale. Such corrections would be reminiscent of the non-perturbative Schwarzschild scale quantum effects that are expected to resolve the black hole information problem. Finally, a byproduct of our analysis is a calculation of how perturbative quantum effects alter charged Reissner-Nordstrom black holes.

Reissner–Nordstrom–anti–de Sitter nontopological solitons in broken Einstein-Maxwell-Higgs theory

Results are presented from numerical simulations of the Einstein-Maxwell-Higgs equations with a broken U(1) symmetry. Coherent nontopological soliton solutions are shown to exist that separate an anti--de Sitter (AdS) true vacuum interior from a Reissner-Nordstrom (RN) false vacuum exterior. The stability of these bubble solutions is tested by perturbing the charge of the coherent solution and evolving the time-dependent equations of motion. In the weak gravitational limit, the short-term stability depends on the sign of $(\ensuremath{\omega}/Q){\ensuremath{\partial}}_{\ensuremath{\omega}}Q$, similar to $Q$-balls. The long-term end state of the perturbed solutions demonstrates a rich structure and is visualized using ``phase diagrams.'' Regions of both stability and instability are shown to exist for ${\ensuremath{\kappa}}_{g}\ensuremath{\lesssim}0.015$, while solutions with ${\ensuremath{\kappa}}_{g}\ensuremath{\gtrsim}0.015$ were observed to be entirely unstable. Threshold solutions are shown to demonstrate time-scaling laws, and the space separating true and false vacuum end states is shown to be fractal in nature, similar to oscillons. Coherent states with superextremal charge-to-mass ratios are shown to exist and observed to collapse or expand, depending on the sign of the charge perturbation. Expanding superextremal bubbles induce phase transitions to the true AdS vacuum, while collapsing superextremal bubbles can form nonsingular strongly gravitating solutions with superextremal RN exteriors.

P–v criticality in the extended phase space of a noncommutative geometry inspired Reissner–Nordström black hole in AdS space-time

The P–v criticality and phase transition in the extended phase space of a noncommutative geometry inspired Reissner–Nordstrom (RN) black hole in Anti-de Sitter (AdS) space-time are studied, where the cosmological constant appears as a dynamical pressure and its conjugate quantity is thermodynamic volume of the black hole. It is found that the P–v criticality and the small black hole/large black hole phase transition appear for the noncommutative RN-AdS black hole. Numerical calculations indicate that the noncommutative parameter affects the phase transition as well as the critical temperature, horizon radius, pressure and ratio. The critical ratio is no longer universal, which is different from the result in the van de Waals liquid–gas system. The nature of phase transition at the critical point is also discussed. Especially, for the noncommutative geometry inspired RN-AdS black hole, a new thermodynamic quantity $$\varPsi $$ conjugate to the noncommutative parameter $$\theta $$ has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.

Dirac equation in Reissner-Nordstrom metric

Dirac equation in Reissner-Nordstrom metric

Hawking Radiation-Quasinormal Modes Correspondence for Large AdS Black Holes

It is well-known that the nonstrictly thermal character of the Hawking radiation spectrum generates a natural correspondence between Hawking radiation and black hole quasinormal modes. This main issue has been analyzed in the framework of Schwarzschild black holes, Kerr black holes, and nonextremal Reissner-Nordstrom black holes. In this paper, by introducing the effective temperature, we reanalyze the nonstrictly thermal character of large AdS black holes. The results show that the effective mass corresponding to the effective temperature is approximatively the average one in any dimension. And the other effective quantities can also be obtained. Based on the known forms of frequency in quasinormal modes, we reanalyze the asymptotic frequencies of the large AdS black hole in three and five dimensions. Then we get the formulas of the Bekenstein-Hawking entropy and the horizon’s area quantization with functions of the quantum “overtone” number n.

Obtaining mass parameters of compact objects from redshifts and blueshifts emitted by geodesic particles around them

The mass parameters of compact objects such as Boson Stars, Schwarzschild, Reissner Nordstrom and Kerr black holes are computed in terms of the measurable redshift-blueshift (zred, zblue) of photons emitted by particles moving along circular geodesics around these objects and the radius of their orbits. We found bounds for the values of (zred, zblue) that may be observed. For the case of Kerr black hole, recent observational estimates of SrgA\* mass and rotation parameter are employed to determine the corresponding values of these red-blue shifts.

Stability of charged thin shell wormhole supported by polytropic gas

In the framework of Darmois-Israel formalism, the general equations describing the motion of thin shell wormhole with a general form of equation of state of a polytropic gas are derived. The mechanical stability analysis of thin shell wormhole with charge in Reissner–Nordstrom (RN) to linearized spherically symmetric perturbation about static equilibrium solution is carried out.

Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole

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.

Action growth for AdS black holes

Recently a Complexity-Action (CA) duality conjecture has been proposed, which relates the quantum complexity of a holographic boundary state to the action of a Wheeler-DeWitt (WDW) patch in the anti-de Sitter (AdS) bulk. In this paper we further investigate the duality conjecture for stationary AdS black holes and derive some exact results for the growth rate of action within the Wheeler-DeWitt (WDW) patch at late time approximation, which is supposed to be dual to the growth rate of quantum complexity of holographic state. Based on the results from the general D-dimensional Reissner-Nordström (RN)-AdS black hole, rotating/charged Bañados-Teitelboim-Zanelli (BTZ) black hole, Kerr-AdS black hole and charged Gauss-Bonnet-AdS black hole, we present a universal formula for the action growth expressed in terms of some thermodynamical quantities associated with the outer and inner horizons of the AdS black holes. And we leave the conjecture unchanged that the stationary AdS black hole in Einstein gravity is the fastest computer in nature.

Surface area products for Kerr-Taub-NUT space-time

We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four-dimensional Lorentzian geometry. We compare and contrasted these properties with the properties of Reissner Nordstrøm (RN) BH and Kerr BH. We focus on “area product”, “entropy product”, “irreducible mass product” of the event horizon and Cauchy horizons. Due to mass dependence, we speculate that these products have no nice quantization feature. Nor do they have any universal property. We further observe that the first law of BH thermodynamics and Smarr-Gibbs-Duhem relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to the presence of the non-trivial NUT charge which makes the space-time be asymptotically non-flat, in contrast with RN BH and Kerr BH. Another reason for the failure is that Lorentzian TN and Lorentzian KTN geometries contain Dirac-Misner–type singularity, which is a manifestation of a non-trivial topological twist of the manifold. The black-hole mass formula and Christodoulou-Ruffini mass formula for TN and KTN BHs are also computed. These thermodynamic product formulae give us further understanding of the nature of inner as well as outer BH entropy at the microscopic level.

Violations of the Kerr and Reissner-Nordström bounds: Horizon versus asymptotic quantities

A central feature of the most elementary rotating black hole (BH) solution in General Relativity is the Kerr bound, which, for vacuum Kerr BHs, can be expressed either in terms of the ADM or the horizon "charges". This bound, however, is not a fundamental properties of General Relativity and stationary, asymptotically flat, regular (on and outside an event horizon) BHs are known to violate the Kerr bound, both in terms of their ADM and horizon quantities. Examples include the recently discovered Kerr BHs with scalar or Proca hair. Here, we point the fact that the Kerr bound in terms of horizon quantities is also violated by well-known rotating and charged solutions, known in closed form, such as the Kerr-Newman and Kerr-Sen BHs. For the former, moreover, we observe that the Reissner-Nordstrom (RN) bound is also violated in terms of horizon quantities, even in the static (i.e RN) limit. For the latter, by contrast, the existence of charged matter outside the horizon, allows a curious invariance of the charge to mass ratio, between ADM and horizon quantities. Regardless of the Kerr bound violation, we show that in all case, the event horizon linear velocity never exceeds the speed of light. Finally, we suggest a new type of informative parameterization for BH spacetimes where part of the asymptotic charges is supported outside the horizon.

Partial wave analysis of the Dirac fermions scattered from Reissner–Nordström charged black holes

The asymptotic form of Dirac spinors in the field of the Reissner-Nordstrom black hole are derived for the scattering states (with $E>mc^2$) obtaining the phase shifts of the partial wave analysis of Dirac fermions scattered from charged black holes. The elastic scattering and absorption are studied giving analytic formulas for the partial amplitudes and cross sections. A graphical study is performed for analysing the differential cross section (forward/backward scattering) and the polarization degree as functions of scattering angle.

Stability analysis and quasinormal modes of Reissner–Nordstrøm space-time via Lyapunov exponent

We explicitly derive the proper-time (τ) principal Lyapunov exponent (λ p ) and coordinate-time (t) principal Lyapunov exponent (λ c ) for Reissner–Nordstrøm (RN) black hole (BH). We also compute their ratio. For RN space-time, it is shown that the ratio is $({\lambda _{p}}/{\lambda _{c}})={r_{0}}/{\sqrt {{r_{0}^{2}}-3Mr_{0}+2Q^{2}}}$ for time-like circular geodesics and for Schwarzschild BH, it is $({\lambda _{p}}/{\lambda _{c}})={\sqrt {r_{0}}}/{\sqrt {r_{0}-3M}}$ . We further show that their ratio λ p /λ c may vary from orbit to orbit. For instance, for Schwarzschild BH at the innermost stable circular orbit (ISCO), the ratio is $({\lambda _{p}}/{\lambda _{c}})|_{r_{\text {ISCO}}=6M}=\sqrt {2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $({\lambda _{p}}/{\lambda _{c}})|_{r_{\mathrm {m}\mathrm {b}}=4M}=2$ . Similarly, for extremal RN BH, the ratio at ISCO is $({\lambda _{p}}/{\lambda _{c}})|_{r_{\text {ISCO}}=4M}={2\sqrt {2}}/{\sqrt {3}}$ . We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit, the real and imaginary parts of the quasinormal modes of RN BH is given by the frequency and instability time-scale of the unstable null circular geodesics.

Phases of global AdS black holes

We study the phases of gravity coupled to a charged scalar and gauge field in an asymptotically Anti-de Sitter spacetime ($AdS_4$) in the grand canonical ensemble. For the conformally coupled scalar, an intricate phase diagram is charted out between the four relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy black hole. The nature of the phase diagram undergoes qualitative changes as the charge of the scalar is changed, which we discuss. We also discuss the new features that arise in the extremal limit.

Superradiantly stable non-extremal Reissner–Nordström black holes

The superradiant stability is investigated for non-extremal Reissner-Nordstrom black hole. We use an algebraic method to demonstrate that all non-extremal Reissner-Nordstrom black holes are superradiantly stable against a charged massive scalar perturbation. This improves the results obtained before for non-extremal Reissner-Nordstrom black holes.

Instability of the de Sitter Reissner–Nordstrom black hole in the expansion

We study the large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that the de Sitter Reissner–Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than a critical charge in a higher dimension. Furthermore, we find that there is a nontrivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black holes. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.

Black holes and gravitational waves in models of minicharged dark matter

In viable models of minicharged dark matter, astrophysical black holes might be charged under a hidden U(1) symmetry and are formally described by the same Kerr-Newman solution of Einstein-Maxwell theory. These objects are unique probes of minicharged dark matter and dark photons. We show that the recent gravitational-wave detection of a binary black-hole coalescence by aLIGO provides various observational bounds on the black hole's charge, regardless of its nature. The pre-merger inspiral phase can be used to constrain the dipolar emission of (ordinary and dark) photons, whereas the detection of the quasinormal modes set an upper limit on the final black hole's charge. By using a toy model of a point charge plunging into a Reissner-Nordstrom black hole, we also show that in dynamical processes the (hidden) electromagnetic quasinormal modes of the final object are excited to considerable amplitude in the gravitational-wave spectrum only when the black hole is nearly extremal. The coalescence produces a burst of low-frequency dark photons which might provide a possible electromagnetic counterpart to black-hole mergers in these scenarios.

Horizon structure of rotating Einstein–Born–Infeld black holes and shadow

We investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity ($\beta \rightarrow \infty$). We find that for a given $\beta$, mass $M$ and charge $Q$, there exist critical spinning parameter $a_{E}$ and $r_{H}^{E}$, which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and $a_{E}$ decreases and $r_{H}^{E}$ increases with increase in the Born-Infeld parameter $\beta$. While $a<a_{E}$ describe a non-extremal Einstein-Born-Infeld black hole with outer and inner horizons. Similarly, the effect of $\beta$ on infinite redshift surface and in turn on ergoregion is also included. It is well known that a black hole can cast a shadow as an optical appearance due to its strong gravitational field. We also investigate the shadow cast by the non-rotating ($a=0$) Einstein-Born-Infeld black hole and demonstrate that the null geodesic equations can be integrated that allows us to investigate the shadow cast by a black hole which is found to be a dark zone covered by a circle. Interestingly, the shadow of the Einstein-Born-Infeld black hole is slightly smaller than for the Reissner-Nordstrom black hole. F urther, the shadow is concentric circles whose radius decreases with increase in value of parameter $\beta$.

Radiation of charged black holes and modified dispersion relation

We investigate the effects of a modified dispersion relation proposed by Majhi and Vagenas on the Reissner-Nordstrom black hole thermodynamics in a universe with large extra dimensions. It is shown that entropy, temperature and heat capacity receive new corrections and charged black holes in this framework have less degrees of freedom and decay faster compared to black holes in the Hawking picture. We also study the emission rate of black hole and compare our results with other quantum gravity approaches. In this regard, the existence of the logarithmic prefactor and the relation between dimensions and charge are discussed. This procedure is not only valid for a single horizon spacetime but it is also valid for the spacetimes with inner and outer horizons.

Quasinormal modes of extremal black holes

The continued fraction method (also known as Leaver's method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordstrom black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordstrom black hole and to neutral massless perturbations around an extremal Kerr black hole. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed.