Gravitational wave observations of the near-horizon region of black holes lend insight into the quantum nature of gravity. In particular, gravitational wave echoes have been identified as a potential signature of quantum gravity-inspired structure near the horizon. In this paper, we connect such observables to the language of black hole microstates in string theory and holography. To that end, we propose a toy model describing the AdS$_3$ near-horizon region of five-dimensional black holes, inspired by earlier work of Solodukhin. This model captures key features of recently constructed microstate geometries, and allows us to make three observations. First, we relate the language of AdS/CFT, in particular the holographic retarded two-point correlator, to effective parameters modeling the structure that are used in flat space gravitational wave literature. Second, we find that for a typical microstate, the `cap' of the microstructure is exponentially close to the horizon, making it an effective sub-Planckian correction to the black hole geometry, although the microstate geometry itself is classical. Third, using a microcanonical ensemble average over geometries, we find support for the claim that the gravitational wave echo amplitude in a typical quantum microstate of the black hole is exponentially suppressed by the black hole entropy.
We review the approach to quantum gravity based on supersymmetry, strings, and holography. This includes a survey of black holes in higher-dimensions, supersymmetry and supergravity, as well as string theory, black hole microstates, and the gauge/gravity duality. This presentation will appear as a chapter in "General Relativity and Gravitation: A Centennial Perspective", to be published by Cambridge University Press.
We study the microstates of the ``small'' black hole in the $\half$-BPS sector of AdS$_5\times S^5$, the superstar of Myers and Tafjord, using the powerful holographic description provided by LLM. The system demonstrates the inherently statistical nature of black holes, with the geometry of Myer and Tafjord emerging only after averaging over an ensemble of geometries. The individual microstate geometries differ in the highly non-trivial topology of a quantum foam at their core, and the entropy can be understood as a partition of $N$ units of flux among 5-cycles, as required by flux quantizatio…
We study information theoretic properties of planar black hole microstates in 2 + 1 dimensional asymptotically anti-de Sitter spacetime, modeled by black holes with an end-of-the-world brane behind the horizon. The von Neumann entropy of sufficiently large subregions in the dual CFT exhibits a time-dependent phase, which from a doubly-holographic perspective corresponds to the appearance of quantum extremal islands in the brane description. Considering the case where dilaton gravity is added to the brane, we show that tuning the associated couplings affects the propagation of information in th…
Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In this paper, we show that, by using supersymmetric localization, the gravitational path integral for $\frac{1}8$-BPS black holes in $\mathcal{N}=8$ supergravity reproduces the index obtained in the string theory construction of such black holes, including all non-perturbatively suppressed geometries. A more refined argument then shows that, not only the black hole index, but also the total number of black hole microstates within an energy window above extr…
We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the b…
In these lectures I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimensions equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS$_4$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS$_5$ black holes.
Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as "superstrata" provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point funct…
In this paper we construct a detailed map from pure and mixed half-BPS states of the D1-D5 system to half-BPS solutions of type IIB supergravity. Using this map, we can see how gravity arises through coarse graining microstates, and we can explicitly confirm the microscopic description of conical defect metrics, the M=0 BTZ black hole and of small black rings. We find that the entropy associated to the natural geometric stretched horizon typically exceeds that of the mixed state from which the geometry was obtained.
Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of …
We study the properties of gravitational system in finite regions bounded by gravitational screens. We present the detail construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy and viscous stress tensor, while the conservations are analogs of non-equilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and non-equilibri…
Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of corner conditions that also must be satisfied where the initial data surface hits the boundary. These are well known to mathematical relativists, but to make them more widely known we give a simple explanation of why these conditions exist and discuss some of their consequences. An example is give…
We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravit…
Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amp…
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
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…
This paper explores construction of gauge (diffeomorphism)-invariant observables in anti de Sitter (AdS) space and the related question of how to find a "holographic map" providing a quantum equivalence to a boundary theory. Observables are constructed perturbatively to leading order in the gravitational coupling by gravitationally dressing local field theory operators in order to solve the gravitational constraints. Many such dressings are allowed and two are explicitly examined, corresponding to a gravitational line and to a Coulomb field; these also reveal an apparent role for more general …
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universa…
Space-based next-generation interferometers propose to measure the Lyapunov exponents of the nearly bound geodesics that comprise the photon ring surrounding the black hole M87*. We argue that these classical Lyapunov exponents equal the quantum Ruelle resonances describing the late-time approach to thermal equilibrium of the quantum microstate holographically dual to any Kerr black hole such as M87*. Moreover, we identify "near-ring regions" in the phase space of fields propagating on Kerr that exhibit critical behavior, including emergent conformal symmetries. These are analogues for sub-ext…
We examine the interplay between recent advances in quantum gravity and the problem of turbulence. In particular, we argue that in the gravitational context the phenomenon of turbulence is intimately related to the properties of spacetime foam. In this framework we discuss the relation of turbulence and holography and the interpretation of the Kolmogorov scaling in the quantum gravitational setting.
We formulate a version of the information paradox in de Sitter spacetime and show that it is solved by the emergence of entanglement islands in the context of the DS/dS correspondence; in particular, the entanglement entropy of a subregion obeys a time-dependent Page curve. Our construction works in general spacetime dimensions and keeps the graviton massless. We interpret the resulting behavior of the entanglement entropy using double holography. It suggests that the spatial distribution of microscopic degrees of freedom depends on descriptions, as in the case of a black hole. In the static (…
Recently, a codimension two holography called wedge holography is proposed as a generalization of AdS/CFT. It is conjectured that a gravitational theory in $d+1$ dimensional wedge spacetime is dual to a $d-1$ dimensional CFT on the corner of the wedge. In this paper, we give an exact construction of the gravitational solutions for wedge holography from the ones in AdS/CFT. By applying this construction, we prove the equivalence between wedge holography and AdS/CFT for vacuum Einstein gravity, by showing that the classical gravitational action and thus the CFT partition function in large N limi…
The vacuum must contain virtual fluctuations of black hole microstates for each mass $M$. We observe that the expected suppression for $M\gg m_p$ is counteracted by the large number $Exp[S_{bek}]$ of such states. From string theory we learn that these microstates are extended objects that are resistant to compression. We argue that recognizing this `virtual extended compression-resistant' component of the gravitational vacuum is crucial for understanding gravitational physics. Remarkably, such virtual excitations have no significant effect for observable systems like stars, but they resolve tw…
If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling $G$. The zero coupling limit gives ordinary qua…
In the action-complexity proposal there are two different methods to regularize the gravitational on-shell action, which are equivalent in the framework of AdS/CFT. In this paper, we want to study the equivalence of them for a pure BTZ black hole microstate. The microstate is obtained from a two-sided BTZ black hole truncated by a dynamical timelike ETW brane. Moreover, it is dual to a finite energy pure state in a two-dimensional CFT. We show that if one includes the timelike counterterms inspired by holographic renormalization as well as the Gibbons-Hawking-York term on the timelike boundary…
It is conventionally believed that if a ball of matter of mass $M$ has a radius close to $2GM$ then it must collapse to a black hole. But string theory microstates (fuzzballs) have no horizon or singularity, and they do {\it not} collapse. We consider two simple examples from classical gravity to illustrate how this violation of our intuition happens. In each case the `matter' arises from an extra compact dimension, but the topology of this extra dimension is not trivial. The pressure and density of this matter diverge at various points, but this is only an artifact of dimensional reduction; t…
We consider the microcanonical ensemble of black holes in gravitational theories in asymptotically anti-de Sitter spacetime with a conformal field theory dual. We argue that typical quantum black hole states show no violations of general covariance on the horizon.
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to RG flows between UV and IR CFTs. We compute the holographic QFT contribution to the gravitational effective action for 4d Einstein manifold backgrounds. We find that for a given value of the cosmological constant $λ$, there generically exist two backreacted constant-curvature solutions, as long as $λ< λ_{\textrm{max}} \sim M_p^2 / N^2$, otherwise n…
In our previous study [1] (1311.6540), we figured out that the thermodynamics of the near extremal black $p$-branes can be explained as the collective motions of gravitationally interacting elementary $p$-branes (the $p$-soup proposal). We test this proposal in the near-extremal D1-D5 and D1-D5-P black holes and show that their thermodynamics also can be explained in a similar fashion, i.e. via the collective motions of the interacting elementary D1-branes and D5-branes (and waves). It may imply that the microscopic origins of these intersecting black branes and the black $p$-brane are explain…
This thesis is divided in two separate parts, the first concerned with gravitational aspects of Lovelock theories, the second with some of their holographic applications.
We consider a holographic study of coupling dependent gravitational waves produced by the cosmic first order QCD phase transition at finite baryochemical potential. In the dual description, the first-order QCD phase transition corresponds to the first-order Hawking-Page phase transition in Gauss-Bonnet gravity. At intermediate coupling, we obtain key quantities characterizing the gravitational wave energy density spectrum. We then find that the gravitational waves might be detected for sufficiently large Gauss-Bonnet coupling, while sound waves play an important role in the spectrum. We also c…
Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and non-perturbative quantum gravity. In perturbation theory about an asymptotically flat collapsing black hole, the algebra generated by asymptotic fields on future null infinity within any neighborhood of spacelike infinity contains a complete set of observables. Assuming that the same algebra remains complete at the non-perturbative quantum level, we argue that either 1) th…
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in th…
Consistent with cosmological constraints, there are scenarios with the large lepton asymmetry which can lead to the finite baryochemical potential at the cosmic QCD phase transition scale. In this paper, we investigate this possibility in the holographic models. Using the holographic renormalization method, we find the first order Hawking-Page phase transition, between Reissner-Nordstr$\rm\ddot{o}$m AdS black hole and thermal charged AdS space, corresponding to the de/confinement phase transition. We obtain the gravitational wave spectra generated during the evolution of bubbles for a range of…
First-quantized propagation in quantum gravitational AdS$_3$ backgrounds can be exactly reconstructed using CFT$_2$ data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, $\langle ϕ_L \mathcal{O}_L \mathcal{O}_H \mathcal{O}_H\rangle$, at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical obs…
We show that extremal black holes have zero entropy by pointing out a simple fact: they are time-independent throughout the spacetime and correspond to a single classical microstate. We show that non-extremal black holes, including the Schwarzschild black hole, contain a region hidden behind the event horizon where all their Killing vectors are spacelike. This region is nonstationary and the time $t$ labels a continuous set of classical microstates, the phase space $[\,h_{ab}(t), P^{ab}(t)\,]$, where $h_{ab}$ is a three-metric induced on a spacelike hypersurface $Σ_t$ and $P^{ab}$ is its momen…
Microstate geometries in string theory replace the black-hole horizon with a smooth geometric "cap" at the horizon scale. In geometries constructed using superstratum technology, this cap has the somewhat surprising property that induces very large tidal deformations on infalling observers that are far away from it. We find that this large-distance amplification of the tidal effects is also present in horizonless microstate geometries constructed as bubbling solutions, but can be tamed by suitably arranging the bubbles to reduce the strength of some of the gravitational multipole moments. Howe…
The entropy of a class of asymptotically AdS$_4$ magnetically charged BPS black holes can be obtained by extremizing the topologically twisted index of the dual three-dimensional field theory. This principle is known as $\mathcal{I}$-extremization. A gravitational dual of $\mathcal{I}$-extremization for a class of theories obtained by twisted compactifications of M2-branes living at a Calabi-Yau four-fold has been recently proposed. In this paper we investigate the relation between the two extremization principles. We show that the two extremization procedures are equivalent for theories witho…
Wormholes are intriguing classical solutions in General Relativity, that have fascinated theoretical physicists for decades. In recent years, especially in Holography, gravitationalWormhole geometries have found a new life in many theoretical ideas related to quantum aspects of gravity. These ideas primarily revolve around aspects of quantum entanglement and quantum information in (semi-classical) gravity. This is an introductory and pedagogical review of Wormholes and their recent applications in Gauge-Gravity duality and related ideas.
We introduce a prescription to compute the entanglement entropy of Galilean conformal field theories by combining gravitational anomalies and an İnönü-Wigner contraction. We find that our expression for the entanglement entropy in the thermal limit reproduces the Cardy formula for Galilean conformal field theories. Using this proposal, we calculate the entanglement entropy for a class of Galilean conformal field theories, which are believed to be dual to three-dimensional flat-space cosmological solutions. These geometries describe expanding (contracting) universes and can be viewed as the fla…
We examine certain two-charge supersymmetric states with spin in five-dimensional string theories which can be viewed as small black rings when the gravitational coupling is large. Using the 4D-5D connection, these small black rings correspond to four-dimensional non-spinning small black holes. Using this correspondence, we compute the degeneracy of the microstates of the small black rings exactly and show that it is in precise agreement with the macroscopic degeneracy to all orders in an asymptotic expansion. Furthermore, we analyze the five-dimensional small black ring geometry and show qual…
We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses…
A new version of holographic principle for cosmology is proposed, which dictates that particle entropy within `cosmological apparent horizon' should not exceed gravitational entropy associated with the apparent horizon. It is shown that, in the Friedman-Robertson-Walker (FRW) cosmology, the open Universe as well as a restricted class of flat cases are compatible with the principle, whereas closed Universe is not. It is also found that inflationary Universe after the big-bang is incompatible with the cosmic holography.
This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory. To this aim, important ingredients are holography and supersymmetric localization. Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on $Σ_\mathfrak{g} \times T^{n}$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory. This defines…
The holographic description of the three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy-momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the usual Hawking temperature, and it is found that the usual Gibbons-Hawking entropy is modified. It is remarked that, due to the gravitationa…
The formation of marginally trapped surfaces in the off-center collision of two shock waves on AdS_D (with D=4,5,6,7 and 8) is studied numerically. We focus on the case when the two waves collide with nonvanishing impact parameter while the sources are located at the same value of the holographic coordinate. In all cases a critical value of the impact parameter is found above which no trapped surface is formed. The numerical results show the existence of a simple scaling relation between the critical impact parameter and the energy of the colliding waves. Using the isometries of AdS_D we relat…
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this correspondence from the viewpoint of entanglement entropy and information metric. The Cramer-Rao bound in quantum estimation theory implies t…
