Extremal Black Holes Research Articles

Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes

We investigate which 4-derivative extensions of Einstein-Maxwell theory admit multi-extremal black hole solutions with gravitational force balanced by Coulomb force. We obtain a set of constraints on the 4-derivative couplings by exploring various probe limits in multi-black hole systems. It turns out that these constraints are tighter than those needed to protect the mass-charge ratio of extremal black holes from higher derivative corrections. In fact, they are so strong that the Majumdar-Papapetrou multi-black solutions are unmodified by the force-free combinations of the 4-derivative couplings. Explicit examples of such 4-derivative couplings are given in 4-and 5-spacetime dimensions. Interestingly these include curvature-squared supergravity actions and the quasi-topological F4 term.

Rotating Bardeen black hole surrounded by perfect fluid dark matter as a particle accelerator

We study the event horizon of a rotating Bardeen black hole surrounded by perfect fluid dark matter and the black hole as a particle accelerator. The black hole is represented by four parameters: mass M, rotation parameter a, dark matter parameter α and magnetic charge g. It is interesting that when we determine the values of magnetic charge g and dark matter parameters α we can get a critical rotation parameter a E and then we get a contour plane with Δ = 0 taking three parameters as coordinates. We also derive the effective potential of the particle and the center-of-mass (CM) energy of the two particles outside the black hole by using the motion equations of the particle in the equatorial plane of the black hole. We find that the CM energy depends not only on the rotation parameter a, but also on the parameters g and α. We discuss the CM energy for two particles colliding at the black hole horizon in the extreme and non-extreme cases, respectively. It is found that the CM energy can become arbitrarily high when the angular momentum of one of the two particles is the critical angular momentum under the background of extreme black holes and there is no such result for non-extreme black holes, because the particles do not reach the black hole horizon when the angular momentum of the particles is critical angular momentum. Therefore, we prove that the rotating Bardeen black hole surrounded by perfect fluid dark matter can be used as a particle accelerator.

Can quasicircular mergers of charged black holes produce extremal black holes?

Can quasicircular mergers of charged black holes produce extremal black holes?

Extremal Kerr Black Holes as Amplifiers of New Physics.

We show that extremal Kerr black holes are sensitive probes of new physics. Stringy or quantum corrections to general relativity are expected to generate higher-curvature terms in the gravitational action. We show that in the presence of these terms, asymptotically flat extremal rotating black holes have curvature singularities on their horizon. Furthermore, near-extremal black holes can have large yet finite tidal forces for infalling observers. In addition, we consider five-dimensional extremal charged black holes and show that higher-curvature terms can have a large effect on the horizon geometry.

Flows of rotating extremal attractor black holes

We investigate the attractor mechanism of five-dimensional extremal rotating black holes in Einstein gravity minimally coupled with a multiplet complex scalar. By imposing regularity on the horizon, we show that the only possible attractor value of the scalar field is zero in our setup and that the local geometry is determined by the Myers-Perry black hole solution. We numerically obtain the extremal AdS black hole solutions interpolating the near horizon geometry to the asymptotic AdS spacetime under the existence of a bare potential of the scalar field. The black hole energy and the angular momenta are discretized for the usual Dirichlet boundary condition. Under the general boundary condition, we also find hairy extremal AdS black holes in which the energy is smaller than that of the extremal Myers-Perry AdS black hole solution for the same angular momentum.

Pole-skipping in rotating BTZ black holes

Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin s = 1/2, 1, 2/3, extending the previous research for s = 0, 2. We derive an analytic full tower of the pole-skipping points of fermionic (s = 1/2) and vector (s = 1) fields by the exact holographic Green’s functions. For the non-extremal black hole, the leading pole-skipping frequency is ωleading = 2πiTh(s − 1 + νΩ)/(1 − Ω2) where Th is the temperature, Ω the rotation, and ν := (∆+ − ∆−)/2, the difference of conformal dimensions (∆±). These are confirmed by another independent method: the near-horizon analysis. For the extremal black hole, we find that the leading pole-skipping frequency can occur at {omega}_{textrm{leading}}^{textrm{extremal}} = −2πiTR(s + 1) only when ν = s + 1, where TR is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit (Th → 0, Ω → 1) of the non-extremal black hole result.

Black hole entropy and moduli-dependent species scale

We provide a moduli-dependent definition of species scale in quantum gravity based on black hole arguments. Concretely, it is derived from a lower bound on the entropy of extremal black holes with higher curvature corrections, which ensures that the black hole can be reliably described within the effective theory. By demanding that our definition coincides with a recent proposal for a moduli-dependent species scale motivated from the topological string, we conclude that the conjecture ZBH=|Ztop|2 relating the black hole to the topological string partition functions should hold, at least within the regime of validity of our analysis.

Near-extremal Freudenthal duality

Freudenthal duality is, as of now, the unique non-linear map on electric-magnetic (e.m.) charges which is a symmetry of the Bekenstein-Hawking entropy of extremal black holes, displaying the Attractor Mechanism (possibly, up to some flat directions) in Maxwell-Einstein-scalar theories in four space-time dimensions and with non-trivial symplectic e.m. duality. In this paper, we put forward an effective approach to a consistent generalization of Freudenthal duality to near-extremal black holes, whose entropy is obtained within a Jackiw-Teitelboim gravity upon dimensional reduction. We name such a generalization near-extremal Freudenthal duality. Upon such a duality, two near-extremal black holes with two different (and both small) temperatures have the same entropy when their e.m. charges are related by a Freudenthal transformation. By exploiting Descartes’ rule of signs as well as Sturm’s Theorem, we show that our formulation of the near-extremal Freudenthal duality is analytical and unique.

Overspinning a rotating black hole in semiclassical gravity with type-A trace anomaly

Recently, Fernandes discovered an analytic solution for rotating black holes in semiclassical gravity induced by the trace anomaly. These solutions exhibit some distinctive characteristics, including a non-spherically symmetric event horizon, the absence of circularity conditions, and violations of the Kerr bound. As a crucial assumption to uphold causality in spacetime, we investigate the validity of the weak cosmic censorship conjecture (WCCC) within this class of solutions with type-A trace anomaly by introducing a test particle on the equatorial plane. Our study reveals three distinct mechanisms that can potentially destroy the event horizon, leading to a violation of the WCCC. Our findings indicate that, with the exception of extremal Kerr, static extremal, and static singular black holes, the WCCC may be violated under the first-order perturbation of the test particle. These results suggest the need for further exploration of modifications to the behavior of the test particle under quantum effects in order to address the violation of the WCCC in this system.

A new class of regular black holes in Einstein Gauss-Bonnet gravity with localized sources of matter

We provide a new regular black hole solution (RBH) in Einstein Gauss-Bonnet (EGB) gravity with localized sources of matter in the energy–momentum tensor. We determine the necessary constraints in order for the solution to be regular. Although we use a specific form for the energy density as a test of proof, these constraints could serve as a recipe for constructing several new RBH solutions in EGB gravity with localized sources. Due to that the usual first law of thermodynamics is not valid for RBH, so we rewrite the first law for EGB, which leads to correct values of entropy and volume. The size of the extremal black hole, whose temperature vanishes, becomes smaller for larger dimensions, whose radius could be of the order of the Planck units, thus the evaporation would stop once the horizon radius contracts up to a value close to the Planck length, which could be related with the apparition of quantum effects. Furthermore, the presence of matter fields in the energy–momentum tensor induces two phase transitions, where there are two regions of stability. This differs from the vacuum EGB solution, where the specific heat is always negative without phase transition as occurs in Schwarzschild black hole.

Traversable wormholes in four dimensions

We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does not lead to causality violations in the ambient space. It can be viewed as a pair of entangled near extremal black holes with an interaction term generated by the exchange of fermion fields. The solution can be embedded in the Standard Model by making its overall size small compared to the electroweak scale.

Challenging event horizons with spin (3/2) fields

We attempt to destroy the event horizons of Kerr black holes by perturbing them with massless spin (3/2) fields. We carry out a detailed analysis by incorporating the explicit form of the absorption probabilities and backreaction effects due to the self energy of the test fields. For extremal and nearly extremal black holes, backreaction effects dominate for perturbations with large magnitudes. However, small perturbations can destroy the event horizons of extremal black holes and drive nearly extremal black holes closer to extremality. Eventually, nearly extremal black holes reach a certain stage where they can be continuously driven to extremality and beyond. Both the cosmic censorship conjecture and the third law of black hole dynamics can be violated by spin (3/2) fields. This directly follows from the fact that fermionic fields do not satisfy the null energy condition. Therefore this result does not contradict with the fact that cosmic censorship and the laws of black hole mechanics remain valid for perturbations satisfying the null energy condition.

Revisiting leading quantum corrections to near extremal black hole thermodynamics

Computing the 4D Euclidean path integral to one-loop order we find the large quantum corrections that govern the behavior of a spherically symmetric non-supersymmetric near-extremal black hole at very low temperature. These corrections appear from the near-horizon geometry of the near-extremal black hole. Using first-order perturbation theory we find that such corrections arise from the zero modes of the extremal background. In the logarithm of the partition function, these correspond to terms involving logarithm of temperature. Part of our result matches with the existing one in literature derived from an effective Schwarzian theory.

Separating the superradiant emission from the Hawking radiation from a rotating black hole

Emission of particles created in the background of a rotating black hole can be greatly amplified taking away rotational energy of a black hole. This amplification affects both particles created near the horizon (due to the Hawing effect), and particles created near the potential barrier far from the horizon. Only the latter effect is called the superradiance in the strict sense. We explicitly calculate the superradiant emission for scalar particles and compare it with the total scalar particle emission (Hawking radiation plus superradiance) to clarify some confusion in the literature. We clearly show that these two emissions are not the same. In particular, superradiance persists even for extremal black holes whose Hawking temperature is zero.

Gauge theories with nontrivial boundary conditions: Black holes

We study the partition function and entropy of U(1) gauge theories with multiple boundaries on the black holes background. The nontrivial boundary conditions allow residual zero longitudinal momentum modes and Wilson lines stretched between boundaries. Topological modes of the Wilson lines and other modes are also analyzed in this paper. We study the behavior of the partition function of the theory in different temperature limits, and find the transitions of dominances of different modes as we vary the temperature. Moreover, we find two different area contributions plus logarithm corrections in the entropy. One being part of the bulk fluctuation modes can be seen for finite-temperature black holes, and the other coming from vacuum degeneracy can only be seen in the superlow temperature limit. We have confirmed the mechanism and entropy found in the superlow temperature limit also persist for extremal black holes. The gauge fluctuation on the black hole background might help us understand some fundamental aspects of quantum gravity related to gauge symmetries.

Late-time asymptotics for geometric wave equations with inverse-square potentials

We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations with asymptotically inverse-square potentials on Schwarzschild black holes. This provides a useful toy model setting for introducing methods that are applicable to more general linear and nonlinear geometric wave equations, such as wave equations for electromagnetically charged scalar fields, wave equations on extremal Kerr black holes and geometric wave equations in even space dimensions, where existing proofs for deriving precise late-time asymptotics might not apply. The method we introduce relies on exploiting the spatial decay properties of time integrals of solutions to derive the existence and precise genericity properties of asymptotic late-time tails and obtain sharp, uniform decay estimates in time.

Aretakis hair for extreme Kerr black holes with axisymmetric scalar perturbations

We study the evolution of axially symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments ${\ensuremath{\ell}}^{\ensuremath{'}}$ higher than the least radiative mode, and we measure modes $\ensuremath{\ell}$---and, for the first time, also horizon charges---that are excited by mode-coupling interactions. We then find the Ori-Sela prefactors, a certain quantity that can be evaluated at finite distances, and the Aretakis constant along the event horizon of the extreme Kerr black hole for a sequence of initial data preparations that differ only by their distance from the event horizon. We find that for initial data in the near field there is a linear relationship of the Aretakis constant and the Ori-Sela prefactor. For initial data farther than these, the linear relationship is not universal, and we propose that stronger numerical simulations would be needed to regain linearity. The linear relationship suggests that the Aretakis charge along the event horizon can be measured at a finite distance, thereby extending this type of violation of the no-hair theorems from the least radiative axisymmetric mode also to situations that involve mode coupling.

Holography for people with no time

We study the gravitational description of extremal supersymmetric black holes. We point out that the AdS_2AdS2 near horizon geometry can be used to compute interesting observables, such as correlation functions of operators. In this limit, the Hamiltonian is zero and correlation functions are time independent. We discuss some possible implications for the gravity description of black hole microstates. We also compare with numerical results in a supersymmetric version of SYK. These results can also be interpreted as providing a construction of wormholes joining two extremal black holes. This is the short version of a longer and more technical companion paper [SciPost Phys. 14, 128 (2023)].

Electromagnetic effects on charged particles in a near-horizon-extreme-Kerr geometry

We investigate the motions of charged particles in the near horizon region of an extreme Kerr black hole with weak electromagnetic fields. There is an enhanced symmetry in the near-horizon-extreme-Kerr geometry. We find that when the electromagnetic field respects this enhanced symmetry, which we refer to as the maximally symmetric electromagnetic field, the equations of motion of charged particles get simplified into a set of decoupled first-order differential equations. We discuss the motions of charged particles in two maximally symmetric electromagnetic fields, one being the force-free field and the other being the vacuum fields. Even though the radial motions are similar to the geodesics in near-horizon-extreme-Kerr geometry, the angular motions could be affected by the electromagnetic field significantly. In particular, for the vacuum solution that is produced by a weakly charged black hole, there exist stable vortical motions if the electromagnetic parameter is above the critical value ${\mathfrak{B}}_{c}=\sqrt{3}$. These vortical motions do not cross the equatorial planes, and the charged particles in them radiate nonthermally. We discuss the corresponding astrophysical implications.

Spontaneous pair production near magnetized Reissner-Nordstrom black holes

We investigate the pair production near a (near) extremal magnetized Reissner-Nordstrom black hole. The pair production is shown to exist in the extremal state, which can be interpreted as the Schwinger effect due to the strong field under consideration. To show a correspondence between the growth of the external magnetic field and the scalar absorption, some numerical examples are provided.