Black Holes In Equilibrium Research Articles

Tidal Forces in Majumdar-Papapetrou Spacetimes

Tidal disruption events occur when astrophysical objects are destroyed by black holes due to strong tidal force effects. Tidal forces have been studied in a variety of black hole spacetimes, including Reissner-Nordström and Kerr spacetimes. Despite the vast literature on the subject, tidal forces around black holes in static equilibrium have never been investigated before. The aim of this work is to fill in this gap and explore tidal forces in the Majumdar-Papapetrou spacetime describing two extremely charged binary black holes in equilibrium. We focus on tidal forces associated with radial and circular geodesics of massive neutral particles moving on the plane equidistant to the black holes. In particular, we study the behavior of the tidal forces as a function of the distance from the black holes and as a function of the energy of the geodesics. We also investigate the numerical solutions of the geodesic deviation equation for different initial conditions.

Theory dependence of black hole interior reconstruction and the extended strong subadditivity

An AdS eternal black hole in equilibrium with a finite temperature bath presents a Hawking-like information paradox due to a continuous exchange of radiation with the bath. The non-perturbative gravitational effect, the replica wormhole, cures this paradox by introducing a non-trivial entanglement wedge for the bath after Page time. In this paper, we analyse the theory dependence of this non-perturbative effect by randomising the boundary conditions of some of the bulk matter fields. We explicitly analyse this in JT gravity by introducing a matter CFT in the AdS region with random boundary conditions at the AdS boundary that are drawn from a distribution. Using the island formula and the extended strong subadditivity due to Carlen and Lieb, we show that at late times the black hole interior is contained inside the entanglement wedge of a reference Hilbert space that encodes the information about the random boundary conditions. Consequently, the reconstruction of the black hole interior from the radiation, in particular the region near the singularity, requires a detailed knowledge of the theory.

Extremal stringy black holes in equilibrium at first order in $\alpha'$

We compute the first-order \alpha'α′ corrections to well-known families of heterotic multi-center black-hole solutions in five and four dimensions. The solutions can be either supersymmetric or non-supersymmetric, depending on the relative sign between two of the black-hole charges. For both cases, we find that the equilibrium of forces persists after including the \alpha'α′ corrections, as the existence of multi-center solutions free of unphysical singularities shows. We analyze the possibility of black-hole fragmentation.

Thermal false vacuum decay around black holes

In flat space and at finite temperature, there are two regimes of false vacuum decay in quantum field theory. At low temperature, the decay proceeds through thermally-assisted tunneling described by periodic Euclidean solutions -- bounces -- with non-trivial time dependence. On the other hand, at high temperature the bounces are time-independent and describe thermal jumps of the field over the potential barrier. We argue that only solutions of the second type are relevant for false vacuum decay catalyzed by a black hole in equilibrium with thermal bath. The argument applies to a wide class of spherical black holes, including $d$-dimensional AdS/dS-Schwarzschild black holes and Reissner-Nordstr\"om black holes sufficiently far from criticality. It does not rely on the thin-wall approximation and applies to multi-field scalar theories.

Ergodic equilibration of R\xe9nyi entropies and replica wormholes

We study the behavior of Rényi entropies for pure states from standard assumptions about chaos in the high-energy spectrum of the Hamiltonian of a many-body quantum system. We compute the exact long-time averages of Rényi entropies and show that the quantum noise around these values is exponentially suppressed in the microcanonical entropy. For delocalized states over the microcanonical band, the long-time average approximately reproduces the equilibration proposal of H. Liu and S. Vardhan, with extra structure arising at the order of non-planar permutations. We analyze the equilibrium approximation for AdS/CFT systems describing black holes in equilibrium in a box. We extend our analysis to the situation of an evaporating black hole, and comment on the possible gravitational description of the new terms in our approximation.

Warped information and entanglement islands in AdS/WCFT

We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT2 degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence emerging when the boundary interval is too big relative to the black hole’s inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT2 and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.

Page curves for a family of exactly solvable evaporating black holes

We study the entanglement entropy of a one-parameter family of exactly solvable gravities in the 2-dimensional asymptotically-flat space. The islands and Page curves of eternal, evaporating and bath-removed black holes are investigated. The different theories in this parameter class are identified through field redefinitions which leave the island invariant. The Page transition is found to occur at the first a third of the black hole life time in the evaporating case for this family of solutions. In addition, we consider gluing the equilibrium black hole and the evaporating one along a null trajectory and study the effect of gluing on the islands and Page curves. In the glued space, the island jumps across two different geometries at a certain retarded time. As a result, the Page transition is stretched and split into two separate ones -- the first transition happens when the net entropy generation stops and the second one occurs as the early radiation effectively starts to become purified. Finally, we discuss the issues concerning the inconsistent rates of purification and the paradox related to the state of the radiation.

Quasinormal modes and their overtones at the common horizon in a binary black hole merger

It is expected that all astrophysical black holes in equilibrium are well described by the Kerr solution. Moreover, any black hole far away from equilibrium, such as one initially formed in a compact binary merger or by the collapse of a massive star, will eventually reach a final equilibrium Kerr state. At sufficiently late times in this process of reaching equilibrium, we expect that the black hole is modeled as a perturbation around the final state. The emitted gravitational waves will then be damped sinusoids with frequencies and damping times given by the quasinormal mode spectrum of the final Kerr black hole. An observational test of this scenario, often referred to as black hole spectroscopy, is one of the major goals of gravitational wave astronomy. It was recently suggested that the quasinormal mode description including the higher overtones might hold even right after the remnant black hole is first formed. At these times, the black hole is expected to be highly dynamical and nonlinear effects are likely to be important. In this paper we investigate this remarkable scenario in terms of the horizon dynamics. Working with high accuracy simulations of a simple configuration, namely the head-on collision of two nonspinning black holes with unequal masses, we study the dynamics of the final common horizon in terms of its shear and its multipole moments. We show that they are indeed well described by a superposition of ringdown modes as long as a sufficiently large number of higher overtones are included. This description holds even for the highly dynamical final black hole shortly after its formation. We discuss the implications and caveats of this result for black hole spectroscopy and for our understanding of the approach to equilibrium.

Entanglement islands in higher dimensions

It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for ``islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.

Stationary Black Holes and Light Rings.

The ringdown and shadow of the astrophysically significant Kerr black hole (BH) are both intimately connected to a special set of bound null orbits known as light rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this Letter we prove the following theorem. A stationary, axisymmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a nonextremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes C^{2} smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultracompact object must admit an even number of nondegenerate LRs, one of which is stable.

Information radiation in BCFT models of black holes

In this note, following [1–3], we introduce and study various holographic systems which can describe evaporating black holes. The systems we consider are boundary conformal field theories for which the number of local degrees of freedom on the boundary (cbdy) is large compared to the number of local degrees of freedom in the bulk CFT (cbulk). We consider states where the boundary degrees of freedom on their own would describe an equilibrium black hole, but the coupling to the bulk CFT degrees of freedom allows this black hole to evaporate. The Page time for the black hole is controlled by the ratio cbdy/cbulk. Using both holographic calculations and direct CFT calculations, we study the evolution of the entanglement entropy for the subset of the radiation system (i.e. the bulk CFT) at a distance d > a from the boundary. We find that the entanglement entropy for this subsystem increases until time a + tPage and then undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior. Remarkably, this occurs even if the radiation system is initially at the same temperature as the black hole so that the two are in thermal equilibrium. In this case, even though the black hole does not lose energy, it “radiates” information through interaction with the radiation system until the radiation system contains enough information to reconstruct the black hole interior.

EHT Constraint on the Ultralight Scalar Hair of the M87 Supermassive Black Hole

Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such a process, however, is only efficient if resonant—when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field black hole equilibrium state—a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass μ ∼ 10 − 20 eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty.

Scattering of uncharged particles in the field of two extremely charged black holes

We investigate the motion of uncharged particles scattered by a binary system consisting of extremely charged black holes in equilibrium as described by the Majumdar-Papapetrou solution. We focus on unbound orbits confined to the plane containing both black holes. We consider the two complementary situations of particles approaching the system along a direction parallel to the axis where the black holes are displaced and orthogonal to it. We numerically compute the scattering angle as a function of the particle's conserved energy parameter, which provides a gauge-invariant information of the scattering process. We also study the precession of a test gyroscope along such orbits and evaluate the accumulated precession angle after a full scattering, which is another gauge-invariant quantity.

Analogies between the Black Hole Interior and the Type II Weyl Semimetals

In the Painleve–Gullstrand (PG) reference frame, the description of elementary particles in the background of a black hole (BH) is similar to the description of non-relativistic matter falling toward the BH center. The velocity of the fall depends on the distance to the center, and it surpasses the speed of light inside the horizon. Another analogy to non-relativistic physics appears in the description of the massless fermionic particle. Its Hamiltonian inside the BH, when written in the PG reference frame, is identical to the Hamiltonian of the electronic quasiparticles in type II Weyl semimetals (WSII) that reside in the vicinity of a type II Weyl point. When these materials are in the equilibrium state, the type II Weyl point becomes the crossing point of the two pieces of the Fermi surface called Fermi pockets. It was previously stated that there should be a Fermi surface inside a black hole in equilibrium. In real materials, type II Weyl points come in pairs, and the descriptions of the quasiparticles in their vicinities are, to a certain extent, inverse. Namely, the directions of their velocities are opposite. In line with the mentioned analogy, we propose the hypothesis that inside the equilibrium BH there exist low-energy excitations moving toward the exterior of the BH. These excitations are able to escape from the BH, unlike ordinary matter that falls to its center. The important consequences to the quantum theory of black holes follow.

Black hole binaries: Ergoregions, photon surfaces, wave scattering, and quasinormal modes

Closed photon orbits around isolated black holes are related to important aspects of black hole physics, such as strong lensing, absorption cross section of null particles and the way that black holes relax through quasinormal ringing. When two black holes are present -- such as during the inspiral and merger events of interest for gravitational-wave detectors -- the concept of closed photon orbits still exists, but its properties are basically unknown. With these applications in mind, we study here the closed photon orbits of two different static black hole binaries. The first one is the Majumdar-Papapetrou geometry describing two extremal, charged black holes in equilibrium, while the second one is the double sink solution of fluid dynamics, which describes (in a curved-spacetime language) two "dumb" holes. For the latter solution, we also characterize its dynamical response to external perturbations, and study how it relates to the photon orbits. In addition, we compute the ergoregion of such spacetime and show that it does not coincide with the event horizon.

Does the black hole shadow probe the event horizon geometry?

There is an exciting prospect of obtaining the shadow of astrophysical black holes (BHs) in the near future with the Event Horizon Telescope. As a matter of principle, this justifies asking how much one can learn about the BH horizon itself from such a measurement. Since the shadow is determined by a set of special photon orbits, rather than horizon properties, it is possible that different horizon geometries yield similar shadows. One may then ask how sensitive is the shadow to details of the horizon geometry? As a case study, we consider the double Schwarzschild BH and analyse the impact on the lensing and shadows of the conical singularity that holds the two BHs in equilibrium -- herein taken to be a strut along the symmetry axis in between the two BHs. Whereas the conical singularity induces a discontinuity of the scattering angle of photons, clearly visible in the lensing patterns along the direction of the strut's location, it produces no observable effect on the shadows, whose edges remain everywhere smooth. The latter feature is illustrated by examples including both equal and unequal mass BHs. This smoothness contrasts with the intrinsic geometry of the (spatial sections of the) horizon of these BHs, which is not smooth, and provides a sharp example on how BH shadows are insensitive to some horizon geometry details. This observation, moreover, suggests that for the study of their shadows, this static double BH system may be an informative proxy for a dynamical binary.

Chaos in charged AdS black hole extended phase space

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare–Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Incoherent transport for phases that spontaneously break translations

We consider phases of matter at finite charge density which spontaneously break spatial translations. Without taking a hydrodynamic limit we identify a boost invariant incoherent current operator. We also derive expressions for the small frequency behaviour of the thermoelectric conductivities generalising those that have been derived in a translationally invariant context. Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions.

Dyonic black holes at arbitrary locations

We construct and study stationary, asymptotically flat multicenter solutions describing regular black holes with non-Abelian hair (colored magnetic-monopole and dyon fields) in two models of mathcal{N}=2 , d = 4 Super-Einstein-Yang-Mills theories: the quadratic model {overline{mathrm{mathbb{C}}mathrm{mathbb{P}}}}^3 and the cubic model ST[2, 6], which can be embedded in 10-dimensional Heterotic Supergravity. These solutions are based on the multicenter dyon recently discovered by one of us, which solves the SU(2) Bogomol’nyi and dyon equations on {mathbb{E}}^3 . In contrast to the well-known Abelian multicenter solutions, the relative positions of the non-Abelian black-hole centers are unconstrained.We study necessary conditions on the parameters of the solutions that ensure the regularity of the metric. In the case of the {overline{mathrm{mathbb{C}}mathrm{mathbb{P}}}}^3 model we show that it is enough to require the positivity of the “masses” of the individual black holes, the finiteness of each of their entropies and their superadditivity. In the case of the ST[2, 6] model we have not been able to show that analogous conditions are sufficient, but we give an explicit example of a regular solution describing thousands of non-Abelian dyonic black holes in equilibrium at arbitrary relative positions.We also construct non-Abelian solutions that interpolate smoothly between just two aDS2×S2 vacua with different radii (dumbbell solutions).

Kerr-Newman black hole in the formalism of isolated horizons

The near horizon geometry of general black holes in equilibrium can be conveniently characterized in the formalism of weakly isolated horizons in the form of the Bondi-like expansions (Krishnan B, Class.\ Quantum Grav.\ 29, 205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has been extensively investigated in the weakly isolated horizon framework, the off-horizon description in the Bondi-like system employed by Krishnan has not been studied. We extend Krishnan's work by explicit, non-perturbative construction of the Bondi-like tetrad in the full Kerr-Newman spacetime. Namely, we construct the Bondi-like tetrad which is parallelly propagated along a nontwisting null geodesic congruence transversal to the horizon and provide all Newman-Penrose scalars associated with this tetrad. This work completes the description of the Kerr-Newman spacetime in the formalism of weakly isolated horizons and is a starting point for the investigation of deformed black holes.