Unitarity implies that the evaporation of microscopic quasi-classical black holes cannot be universal in different particle species. This creates a puzzle, since it conflicts with the thermal nature of quasi-classical black holes, according to which all the species should see the same horizon and be produced with the same Hawking temperatures. We resolve this puzzle by showing that for the microscopic black holes, on top the usual quantum evaporation time, there is a new time-scale which characterizes a purely classical process during which the black hole looses the ability to differentiate among the species, and becomes democratic. We demonstrate this phenomenon in a well-understood framework of large extra dimensions, with a number of parallel branes. An initially non-democratic black hole is the one localized on one of the branes, with its high-dimensional Schwarzschild radius being much shorter than the interbrane distance. Such a black hole seemingly cannot evaporate into the species localized on the other branes, that are beyond its reach. We demonstrate that in reality the system evolves classically in time, in such a way that the black hole accretes the neighboring branes. The end result is a completely democratic static configuration, in which all the branes share the same black hole, and all the species are produced with the same Hawking temperature. Thus, just like their macroscopic counterparts, the microscopic black holes are universal bridges to the hidden sector physics.
We study the evolution of black hole entropy and temperature in collapse scenarios, finding three generic lessons. First, entropy evolution is extensive. Second, at large times, entropy and temperature ring with twice the frequency of the lowest quasinormal mode. Third, the entropy oscillations saturate black hole area theorems in general relativity. The first two features are characteristic of entanglement dynamics in `democratic' models. Solely based on general relativity and Bekenstein-Hawking entropy formula, our results point to democratic models as microscopic theories of black holes. Th…
We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling conjecture. We show that these democratic walks describe well the properties of information spreading in systems in which every degree of freedom interacts with every other degree of freedom, such as Matrix or infinite range models. The argument is based on the analysis of suitably defined `Information fields' ($\mathcal{I}$), which are shown to evolve stochast…
We find double-extreme black holes associated with the special geometry of the Calabi-Yau moduli space with the prepotential F=STU. The area formula is STU-moduli independent and has ${[SL(2,Z)]}^3$ symmetry in space of charges. The dual version of this theory without prepotential treats the dilaton S asymmetric versus T,U-moduli. We display the dual relation between new (STU) black holes and stringy (S|TU) black holes using particular Sp(8, Z) transformation. The area formula of one theory equals that of the dual theory when expressed in terms of dual charges. We analyse the relation between …
The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g. negative specific heat and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon …
We use mergers of microstates to obtain the first smooth horizonless microstate solutions corresponding to a BPS three-charge black hole with a classically large horizon area. These microstates have very long throats, that become infinite in the classical limit; nevertheless, their curvature is everywhere small. Having a classically-infinite throat makes these microstates very similar to the typical microstates of this black hole. A rough CFT analysis confirms this intuition, and indicates a possible class of dual CFT microstates. We also analyze the properties and the merging of microstates c…
We revisit the microscopic description of AdS$_3$ black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS$_3$/CFT$_2$ correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is no…
A surprising new seven-parameter supersymmetric black ring solution of five-dimensional supergravity has recently been discovered. In this paper, M-theory is used to give an exact microscopic accounting of its entropy.
The phase transition of the Gauss-Bonnet AdS black hole has the similar property with the van der Waals thermodynamic system. However, it is determined by the Gauss-Bonnet coefficient α, not only the horizon radius. Furthermore, the phase transition is not the pure one between a big black hole and a small black hole. With this issue, we introduce a new order parameter to investigate the critical phenomenonand to give the microstructure explanation of the Gauss-Bonnet AdS black hole phase transition. And the critical exponents are also obtained. At the critical pointof the Gauss-Bonnet AdS blac…
We discuss a previous attempt at a microscopic counting of the entropy of asymptotically flat non-extremal black-holes. This method used string dualities to relate 4 and 5 dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.
In a recent letter, Cadoni and Mignemi proposed a formulation for the statistical computation of the 2D black holes entropy. We present a criticism about their formulation.
Using the new normalized thermodynamic scalar curvature, we investigate the microstructures and phase transitions of black holes in massive gravity for horizons of various topologies. We find that the graviton mass enhances the repulsive interactions of small black holes and weakens the attractive interactions of large black holes, with possiblity of new repulsive regions for microstructures in phase space. In addition, the repulsive interactions of small black hole are strong for spherical topology, followed by flat and hyperbolic topology; while, the attractive interactions of large black ho…
String theory is used to compute the microscopic entropy for several examples of black holes in compactifications with $N=2$ supersymmetry. Agreement with the Bekenstein-Hawking entropy and the moduli-independent $N=2$ area formula is found in all cases.
We study the dynamics of supertubes in smooth bubbling geometries with three charges and three dipole charges that can describe black holes, black rings and their microstates. We find the supertube Hamiltonian in these backgrounds and show that there exist metastable supertube configurations, that can decay into supersymmetric and non-supersymmetric ones via brane-flux annihilation. We also find stable non-supersymmetric configurations. Both the metastable and the stable non-supersymmetric configuration are expected to describe microstate geometries for non-extremal black holes, and we discuss…
We compute one point functions of chiral primary operators in the D1-D5 orbifold CFT, in classes of states corresponding to microstates of two and three charge black holes. Black hole microstates describable by supergravity solutions correspond to coherent superpositions of states in the orbifold theory and we develop methods for approximating one point functions in such superpositions in the large N limit. We show that microstates built from long strings (large twist operators) have one point functions that are suppressed by powers of N. Accordingly, even when these microstates admit supergra…
We explore the possible microscopic structure of a charged AdS black hole from the quantized viewpoint. A further study shows that some black holes cannot absorb "energy quantum" under certain conditions from the view of quantization. By the quantization of the black hole horizon area, we show the relation between the number of quanta of area and the microscopic degrees of freedom of the black hole. We also interpret a latent heat of thermodynamical phase transition as a transition between the number of quanta of area of large black hole(LBH) and the number of quanta of area of small black hol…
We show that the arguments proposed by Park and Yee against our recent derivation of the statistical entropy of 2D black holes do not apply to the case under consideration
We study how black hole superradiance appears in string microscopic models of rotating black holes. In order to disentangle superradiance from finite-temperature effects, we consider an extremal, rotating D1-D5-P black hole that has an ergosphere and is not supersymmetric. We explain how the microscopic dual accounts for the superradiant ergosphere of this black hole. The bound 0< omega < m Omega_H on superradiant mode frequencies is argued to be a consequence of Fermi-Dirac statistics for the spin-carrying degrees of freedom in the dual CFT. We also compute the superradiant emission rates fro…
In this paper we will give a general introduction to the role of conformal symmetry in the microscopic interpretation of black hole entropy and then compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro algebra of a Liouville theory and using the Cardy formula.
It is shown, using conformal symmetry methods, that one can obtain microscopic interpretation of black hole entropy for general class of higher curvature Lagrangians.
The Gelfand pattern of the reduction of the N-fold tensor product of the fundamental representation of the special unitary group SU(2) by itself is studied in the framework of a finite Heisenberg model with infinite range, where N spins couple to each other with the same strength. The present findings are related to the microstatistics of non-rotating black holes for illustrative purposes.
We derive the leading g_s perturbation of the SUGRA fields generated by a supersymmetric configuration of respectively 1, 2 or 4 D3-branes intersecting at an arbitrary angle via the computation of the string theory disk scattering amplitude of one massless NSNS field interacting with open strings stretched between the branes. The configuration with four branes is expected to be relevant for black hole microstate counting in four dimensions.
Computations in general relativity have revealed an interesting phase diagram for the black hole - black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by `boosting' plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of 4+1 dimensional near-extremal holes and 3+1 dimensional n…
In this article we study correspondence between the microscopic spectrum and macroscopic properties of a class of extremal and non-extremal black branes and outline an origin of the interactions among various microstates of a given black brane configuration from the perspective of an intrinsic Riemannian geometry arising from the coarse graining entropy over a large number of microstates. We have analyzed the state-space geometry in the case of various extremal and non-extremal black branes arising from the string theories, multi-centered black brane configurations, small black holes with frac…
In this review article we describe some of the recent progress towards the construction and analysis of three-charge configurations in string theory and supergravity. We begin by describing the Born-Infeld construction of three-charge supertubes with two dipole charges, and then discuss the general method of constructing three-charge solutions in five dimensions. We explain in detail the use of these methods to construct black rings, black holes, as well as smooth microstate geometries with black hole and black ring charges, but with no horizon. We present arguments that many of these microsta…
The statistical mechanics of black holes arbitrarily far from extremality is modeled by a gas of weakly interacting strings. As an effective low energy description of black holes the model provides a number of highly non-trivial consistency checks and predictions. Speculations on a fundamental origin of the model suggest surprising simplifications in non-perturbative string theory, even in the absence of supersymmetry.
The exact entropy of two-charge supersymmetric black holes in N=4 string theories is computed to all orders using Wald's formula and the supersymmetric attractor equations with an effective action that includes the relevant higher curvature terms. Classically, these black holes have zero area but the attractor equations are still applicable at the quantum level. The quantum corrected macroscopic entropy agrees precisely with the microscopic counting for an infinite tower of fundamental string states to all orders in an asymptotic expansion.
The black-hole information paradox provides a stringent test of would-be theories of quantum gravity. String theory has made significant progress toward a resolution of this paradox, and has led to the fuzzball and microstate geometry programs. The central thesis of these programs is that only string theory has sufficiently many degrees of freedom to resolve black-hole microstructure, and that horizons and singularities are artifacts of attempting to describe gravity using a theory that has too few degrees of freedom to resolve the physics. Fuzzballs and microstate geometries recast black hole…
We extract the leading-order entropy of a four-dimensional extremal black hole in ${\cal N}{=}2$ ungauged supergravity by formulating the CFT$_1$ that is holographically dual to its near-horizon AdS$_2$ geometry, in terms of a rational Calogero model with a known counting formula for the degeneracy of states in its Hilbert space.
We present a new family of asymptotic AdS_3 x S^2 solutions to eleven dimensional supergravity compactified on a Calabi-Yau threefold. They originate from the backreaction of S^2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. We show that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation.
We demonstrate a solution generating technique, modulo some constraints, for a large class of smooth supergravity solutions with the same asymptotic charges as a five dimensional 3-charge BPS black hole or black ring, dual to a D1/D5/P system. These solutions are characterized by a harmonic function with both positive and negative poles, which induces a geometric transition whereby singular sources have disappeared and all of the net charge at infinity is sourced by fluxes through two-cycles joining the poles of the harmonic function.
We show that a class of four-dimensional rotating black holes allow five-dimensional embeddings as black rotating strings. Their near-horizon geometry factorizes locally as a product of the three-dimensional anti-deSitter space-time and a two-dimensional sphere (AdS_3 x S^2), with angular momentum encoded in the global space-time structure. Following the observation that the isometries on the AdS_3 space induce a two-dimensional (super)conformal field theory on the boundary, we reproduce the microscopic entropy with the correct dependence on the black hole angular momentum.
We derive a precise dictionary between micro-state geometries and open string condensates for a large class of excitations of four dimensional BPS black holes realised in terms of D3-branes intersecting on a six-torus. The complete multipole expansion of the supergravity solutions at weak coupling is extracted from string amplitudes involving one massless closed string and multiple open strings insertions on disks with mixed boundary conditions.
We discuss some aspects of the recently discovered BPS black ring solutions in terms of the AdS/CFT correspondence. In the type IIB frame in which the black ring carries the charges of the D1-D5-P system, we propose a microscopic description of the rings in the orbifold CFT governing this system. In our proposal, the CFT effectively splits into two parts: one part captures the supertube-like properties of the ring, and the other captures the entropy. We can also understand the black ring entropy by relating the geometry near the ring to BPS black holes in four dimensions, although this latter …
Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously as we vary the asymptotic values of various moduli fields. Using this fact we argue that the entropy of an extremal black hole in string theory, calculated for a range of values of the asymptotic moduli for which the microscopic theory is strongly coupled, should match the statistical entropy of the same system calculated for a range of values of the asymptotic moduli for which the microscopic theory is weakly coupled. This argument does not rely on supersymmetry and applies equally well to nonsupe…
All known horizonless black-hole microstate geometries correspond to brane sources that acquire a finite size, and hence break the spherical symmetry of the black hole. We construct, for the first time, solutions with zero horizon area that have the same charges as a three-charge F1-NS5-P Type-IIA black hole and preserve this spherical symmetry. The momentum of these solutions is carried by longitudinal D0-D4 density fluctuations inside the NS5-branes. We argue that these solutions should be interpreted as the long-throat limit of a family of smooth, horizonless microstate geometries, called s…
Thermodynamics of the near extremal black p-branes can be described by collective motions of gravitationally interacting branes. This proposal is called the p-soup model. In this paper, we check this proposal in the case of black brane system which is asymptotically Friedmann-Lemaitre-Robertson-Walker universe in an infinite distance. As a result, we can show that the gravitationally interacting branes explain free energy, entropy, temperature and other physical quantities in these systems. This implies that the microstates of this kind of brane system can be also understood in the p-soup mode…
Thermodynamic geometry analysis of interesting Letter [Phys. Rev. Lett. 115, 111302 (2015)] for charged AdS black holes, which is based on studying the Ruppeiner invariant behavior is not correct and the authors made a mistake in calculating this quantity. In the present Letter, we address the correct Ruppeiner scalar curvature and reveal the correct possible microscopic properties of 4-dimensional charged AdS black holes arise from it. Some of these properties have not been discussed in pointed out Letter.
A five-dimensional dyonic black hole in Type-I theory is considered that is extremal but non-supersymmetric. It is shown that the Bekenstein-Hawking entropy of this black hole counts precisely the microstates of a D-brane configuration with the same charges and mass, even though there is no apparent supersymmetric nonrenormalization theorem for the mass. A similar result is known for the entropy at the stretched horizon of electrically charged, extremal, but non-supersymmetric black holes in heterotic string theory. It is argued that classical nonrenormalization of the mass may partially expla…
Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole. The latter statement can be interpreted in two ways. First, at the fully non-perturbative level of AdS/CFT at finite N, it means that cluster decomposition does not hold in the bulk. This may be viewed as a sharp manifestation of the bulk non-locality a…
Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of whic…
We review the status of microscopic counting of rotating black hole degrees of freedom. We present two complementary approaches which both utilize the near-horizon geometry and precisely reproduce the Bekenstein Hawking entropy for near-extreme rotating black holes in D=4 and D=5. The first one, proposed by Strominger, is applicable for the Ramond-Ramond sector and relies on the correspondence between the near-horizon geometry and the conformal field theory on its boundary. The second one (somewhat more heuristic), employs the conformal sigma-model in the Neveu-Schwarz-Neveu-Schwarz sector and…
We review recent results in the study of regular four dimensional BPS black holes in toroidally compactified type II (or M) theory. We discuss the generating solution for this kind of black holes, its microscopic description(s), and compute the corresponding microscopic entropy. These achievements, which provide a description of the fundamental degrees of freedom accounting for the entropy of any regular BPS black hole in the theory under consideration, are inscribed within a research project aimed to the study of the microscopic properties of this kind of solutions in relation to U--duality i…
We provide a universal microscopic counting for the microstates of the asymptotically AdS black holes and black strings that arise as solutions of the half-maximal gauged supergravity in four and five dimensions. These solutions can be embedded in all M-theory and type II string backgrounds with an AdS vacuum and sixteen supercharges and provide an infinite set of examples dual to $\mathcal{N}=2$ and $\mathcal{N}=4$ conformal field theories in four and three dimensions, respectively. The counting is universal and it is performed by either studying the large $N$ limit of the relevant supersymme…
We construct probe solutions in the attractor background of the five-dimensional D1-D5-P black hole which represent near-horizon microstates in the limit of large D1-charge. These generalize the corresponding solutions considered by Gaiotto, Strominger and Yin for the 4-dimensional D0-D4 black hole. Using U-duality and a 4D-5D connection, we argue that the relevant configurations are bound states of D1-branes that have expanded through the Myers effect to form a Kaluza-Klein monopole wrapping the black hole horizon. We show that these branes experience a magnetic field on their moduli space, a…
We compute the topologically twisted index for general $\mathcal{N} = 2$ supersymmetric field theories on $\mathbb{H}_2\times S^1$. We also discuss asymptotically $AdS_4$ magnetically charged black holes with hyperbolic horizon, in four-dimensional $\mathcal{N} = 2$ gauged supergravity. With certain assumptions, put forward by Benini, Hristov and Zaffaroni, we find precise agreement between the black hole entropy and the topologically twisted index, for $ABJM$ theories.
Understanding the microscopic behavior of the black holes ingredients has been one of the important challenges in black holes physics during the past decades. In order to shed some light on the microscopic structure of black holes, in this paper, we explore a recently observed phenomenon for black holes namely reentrant phase transition, by employing the Ruppeiner geometry. Interestingly enough, we observe two properties for the phase behaviour of small black holes that leads to reentrant phase transition. They are correlated and they are of the interaction type. For the range of pressure in w…
The microscopic formula for the degeneracy of BMPV black hole microstates contains a series of exponentially suppressed corrections to the leading Bekenstein Hawking expression. We identify saddle points of the quantum entropy function for the BMPV black hole which are natural counterparts to these corrections and discuss the matching of leading and next-to-leading terms from the microscopic and macroscopic sides in a limit where the black hole charges are large.
We argue that the fundamental "atomic objects" in string theory are themelia: extended objects that have 16 supersymmetries locally. We show that all existing smooth horizonless microstate geometries can be seen as bound states of themelia, and we conjecture that all such bound states with suitable KKM charges will give rise to microstate geometries. We also construct the most general themelion with a three-torus isometry and show that it interpolates between superstrata and the super-maze.
In theories with many copies of the Standard Model virtual black hole exchange may produce effective higher dimensional operators that can be treated below the cutoff scale as fundamental vertices of interspecies non-gravitational interaction. We consider the vertex that couples fermions of one species through magnetic moment to photons of other species, and study the quantum corrections it generates. In particular, we find kinetic mixing between photons of different species produced via fermion loops. Diagonalization of gauge kinetic terms then renders the fermions millicharged under other sp…
Ruppeiner geometry has been found to be a novel promising approach to uncover the microstructure of fluid systems and black holes. In this work, combining with the micro model of the Van der Waals fluid, we shall propose a first microscopic interpretation for the empirical observation of Ruppeiner geometry. Then employing the microscopic interpretation, we disclose the potential microstructure for the anti-de Sitter black hole systems. Of particular interest, we obtain the microscopic interaction potentials for the underlying black hole molecules. This significantly strengthens the study towar…
It is shown that with allowance for nonadditivity the (canonical) distribution for a black hole transforms to a (microcanonical) distribution which depends on nonadditive integrals of the motion and represents a nonlinear function of energy - the square of black hole mass. From a comparison with the standard microcanonical distribution it is found that the statistical weight of black hole should be proportional to the black hole area. A definition of the black hole entropy consistent with the statistical weight is proposed.
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the …
The microcanonical treatment of black holes as opposed to the canonical formulation is reviewed and some major differences are displayed. In particular the decay rates are compared in the two different pictures.
The Ruppeiner geometry of thermodynamic fluctuations provides a powerful diagnostic of black hole microstructures. We investigate this for charged AdS black holes and find that while an attractive microstructure interaction dominates for most parameter ranges, a weak repulsive interaction dominates for small black holes of high temperature. This unique property distinguishes the black hole system from that of a Van der Waals fluid, where only attractive microstructure interactions are found. We also find two other novel universal properties for charged black holes. One is that the repulsive in…
We provide the first explicit proposal for all microstates of generic black holes in three dimensions (of Banados-Teitelboim-Zanelli-type): black hole microstates, termed "horizon fluffs", are a particular class of near horizon soft hairs which have zero energy as measured by the horizon observer and cannot be distinguished by observers at finite distance from the horizon. These states are arranged in orbits of the two-dimensional conformal algebra associated with the asymptotic black hole geometry. We count these microstates using the Hardy-Ramanujan formula for the number of partitions of a …
The microcanonical statistics of the Schwarzschild black holes as well as the Reissner-Nordstr$\sf \ddot{o}$m black holes are analyzed. In both cases we set up the inequalities in the microcanonical density of states. These are then used to show that the most probable configuration in the gases of black holes is that one black hole acquires all of the mass and all of the charge at high energy limit. Thus the black holes obey the statistical bootstrap condition and, in contrast to the other investigation, we see that U(1) charge does not break the bootstrap property.
We show that an extremal Kerr black hole, appropriately lifted to M-theory, can be transformed to a Kaluza-Klein black hole in M-theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M-theory.
