We argue that classical $(α')$ effects qualitatively modify the structure of Euclidean black hole horizons in string theory. While low energy modes experience the geometry familiar from general relativity, high energy ones see a rather different geometry, in which the Euclidean horizon can be penetrated by an amount that grows with the radial momentum of the probe. We discuss this in the exactly solvable SL(2,R)/U(1) black hole, where it is a manifestation of the black hole/Sine-Liouville duality.
We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular space-time geometry. String theory motivates the inclusion of higher derivative terms, which convert these singular classical solutions into regular black holes with finite horizon area. In particular, the supersymmetric attractor equations imply that the central charge, which determines the radius of the $AdS_2\times S^2$ near horizon geometry, acquires a non-vanishing value due to quantum effects. In this case quantum correcti…
We have argued previously, based on the analysis of two-dimensional stringy black holes, that information in stringy versions of four-dimensional Schwarzschild black holes (whose singular regions are represented by appropriate Wess-Zumino-Witten models) is retained by quantum $W$-symmetries when the horizon area is not preserved due to Hawking radiation. It is key that the exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole requires a contribution from $W_\infty$ generators in its vertex function. The latter correspond to del…
Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli理论科学研究院）；MIT Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）
Hawking radiation is computed in different coordinate systems using the method of complex paths. In this procedure the event horizon of the 2D Schwarzschild stringy black hole is treated as a singularity for the semiclassical action functional. After the regularization of the event horizon's singularity the emission/absorption probabilities and the Hawking temperature in the different coordinate representations are derived. The identical results obtained indicate the covariance of the Hawking radiation.
We consider the first laws of thermodynamics for a pair of systems made up of the two horizons of a Kerr-Newman black hole. These two systems are constructed in such a way that we only demand their ``horizon areas'' to be the sum and difference of that of the outer and inner horizons of their prototype. Remarkably, these two copies bear a striking resemblance to the right- and left-movers in string theory and D-brane physics. Our reformulation of the first law of black hole thermodynamics can be thought of as an analogy of thermodynamics of effective string or D-brane models.
We elaborate on the recent claim [arXiv:1702.03583] that non-perturbative effects in $α'$, which are at the core of the FZZ duality, render the region just behind the horizon of the $SL(2,\mathbb{R})_k/U(1)$ black hole singular already at the classical level ($g_s=0$). We argue that the 2D classical $SL(2,\mathbb{R})_k/U(1)$ black hole could shed some light on quantum black holes in higher dimensions including large black holes in $AdS_5\times S^5$.
The target-space interpretation of the exact (in $α'$) reflection coefficient for scattering from Euclidean black-hole horizons in classical string theory is studied. For concreteness, we focus on the solvable $SL(2, \mathbb{R})_k/U(1)$ black hole. It is shown that it exhibits a fascinating UV/IR mixing, dramatically modifying the late-time behavior of general relativity. We speculate that this might play an important role in the black-hole information puzzle, as well as in clarifying features related with the non-locality of Little String Theory.
We study small fluctuations of the stringy wormhole solutions of graviton-dilaton-axion system in arbitrary dimensions. We show under O($d$)-symmetric harmonic perturbation that the Euclidean wormhole solutions are unstable in flat space irrespective of dimensions and in anti de Sitter space of $d=3$.
In this paper we show that it is possible to derive non-perturbative superpotential terms from a stringy instanton without introducing orientifold planes. The instanton is realized by a Euclidean D brane wrapping a non-trivial cycle upon which we also wrap a single space-filling D brane. The standard problem of unwanted neutral fermionic zero modes is evaded by the appearance of couplings to charged bosonic zero modes in the instanton moduli action. Since the Euclidean D brane wraps a cycle which is not associated to any low energy gauge dynamics, it can not be interpreted as an ordinary gauge…
We study the first-order in $α'$ corrections to 4-charge black holes (with the Reissner-Nordström black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU$(2)$ instantons for the h…
The string propagation in the two-dimensional stringy black-hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the lorentzian and euclidean regimes. In the lorentzian case all the physics reduces to a massless scalar particle described by a Klein-Gordon type equation with a singular effective potential. The scattering matrix is found and it reproduces the results obtained by coset CFT techniques. It factorizes into two pieces : an elastic coulombian amplitude and an absorption part. In both parts, an infinite sequence of imaginary poles i…
We argue that non-perturbative $α'$ stringy effects render the Hartle-Hawking state associated with the $SL(2)/U(1)$ eternal black hole singular at the horizon. We discuss implications of this observation on firewalls in string theory.
The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）；Institute for Theoretical Physics, Institute of Physics Universiteit van Amsterdam（阿姆斯特丹大学物理研究所理论物理系）
Black holes are a powerful setting for studying general relativity and theories beyond GR. However, analytical solutions for rotating black holes in beyond-GR theories are difficult to find because of the complexity of such theories. In this paper, we solve for the deformation to the near-horizon extremal Kerr metric due to two example string-inspired beyond-GR theories: Einstein-dilaton-Gauss-Bonnet, and dynamical Chern-Simons theory. We accomplish this by making use of the enhanced symmetry group of NHEK and the weak-coupling limit of EdGB and dCS. We find that the EdGB metric deformation ha…
It is reported that massive scalar fields can form bound states around Kerr black holes [C. Herdeiro, and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)]. These bound states are called scalar clouds, which have a real frequency $ω=mΩ_H$, where $m$ is the azimuthal index and $Ω_H$ is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition $ω=qΦ_H$ for the charged scalar field, where…
We study the quasinormal modes (QNMs) for stringy black holes. By using numerical calculation, the relations between the QNMs and the parameters of black holes are minutely shown. For (1+1)-dimensional stringy black hole, the real part of the quasinormal frequency increases and the imaginary part of the quasinormal frequency decreases as the mass of the black hole increases. Furthermore, the dependence of the QNMs on the charge of the black hole and the flatness parameter is also illustrated. For (1+3)-dimensional stringy black hole, increasing either the event horizon or the multipole index, …
We study the thermodynamical and geometrical behaviour of the black holes that arise as solutions of the heterotic string action. We discuss the near-horizon scaling behaviour of the solutions that are described by two-dimensional Anti-de Sitter Space AdS(2). We find that finite-energy excitations of AdS(2) are suppressed only for scaling limits characterised by a dilaton which is constant near the horizon, whereas this suppression does not occur when the dilaton is non constant.
Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stabilit…
Building upon our previous work on two-dimensional stringy black holes and its extension to spherically-symmetric four-dimensional stringy black holes, we show how the latter retain information. A key rôle is played by an infinite-dimensional $W_\infty$ symmetry that preserves the area of an isolated black-hole horizon and hence its entropy. The exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole necessarily includes a contribution from $W_\infty$ generators in its vertex function. This admixture manifests the transfer of inf…
The ER = EPR correspondence relates a superposition of entangled, disconnected spacetimes to a connected spacetime with an Einstein-Rosen bridge. We construct examples in which both sides may be described by weakly-coupled string theory. The relation between them is given by a Lorentzian continuation of the FZZ duality of the two-dimensional Euclidean black hole CFT in one example, and in another example by continuation of a similar duality that we propose for the asymptotic Euclidean AdS3 black hole. This gives a microscopic understanding of ER = EPR: one has a worldsheet duality between stri…
The model of the bosonic string with the noncommutative world-sheet geometry is proposed in the framework of Fedosov's deformation quantization. The re-interpretation of the model in terms of bosonic string coupled to infinite multiplet of background fields is given and the link to the W-symmetry is discussed. For the case of d=4 Euclidean target space, the stringy counterparts of the Yang-Mills instantons are constructed in both commutative and noncommutative regimes.
It has been argued recently that string theory effects qualitatively modify the effective black hole geometry experienced by modes with radial momentum of order $1/\sqrt{α'}$. At tree level, these $α'$-effects can be explicitly worked out in two-dimensional string theory, and have a natural explanation in the T-dual description as coming from the integration of the zero-mode of the linear dilaton, what yields a contribution that affects the scattering phase-shift in a peculiar manner. It has also been argued that the phase-shift modification has its origin in a region of the moduli space that …
We show that the spectrum of normalizable states on a Euclidean SL(2,R)/U(1) black hole exhibits a duality between oscillator states and wound strings. This duality generalizes the FZZ correspondence, which can be thought of as an identification between a normalizable mode of dilaton gravity and a mode of the tachyon with winding number one around the Euclidean time circle. It implies that normalizable states on a large Euclidean black hole have support at widely separated scales. In particular, localized states that are extended over the cap of the cigar (the Euclidian analog of the black hol…
Negative energy objects generally lead to instabilities and a number of other disturbing behaviors. In particular, negative energy fluxes lead to a breakdown of the classical area theorem for black hole horizons, which can lead to violations of the second law of thermodynamics. The negative energy objects that arise in string theory involve special boundary conditions which remove the perturbative instabilities. We show that they have additional special features which allow them to evade contradiction with the second law. We identify one mechanism which applies for most orientifold planes in s…
The static stationary axially symmetric background ("infinite cosmic string") of the $D=4$ string theory provided with an axion charge is studied in the effective theory approach. The most general exact solution is constructed. It is found that the Kalb-Ramond axion charge, present in the string topology $R^{3} \times S^{1}$, produces nontrivial gravitational field configurations which feature horizons. The corresponding ``no-hair'' theorems are proved which stress uniqueness of black strings. Connection of the solutions with the gauged WZWN sigma model constructions on the world sheet is disc…
We interpret Minkowski black holes as world-sheet {\it spikes } which are related by world-sheet { \it duality} to {\it vortices } that correspond to Euclidean black holes. These world-sheet defects induce defects in the gauge fields of the corresponding coset Wess-Zumino descriptions of spherically-symmetric black holes. The low-temperature target space-time foam is a Minkowski black hole (spike) plasma with confined Euclidean black holes (vortices). The high-temperature phase is a {\it dense} vortex plasma described by a topological gauge field theory on the world-sheet, which possesses enha…
We consider black holes in anti-de Sitter space AdS_{p+2} (p = 2,3,5), which have hyperbolic, flat or spherical event horizons. The $O(α'^3)$ corrections (or the leading corrections in powers of the eleven-dimensional Planck length) to the black hole metrics are computed for the various topologies and dimensions. We investigate the consequences of the stringy or M-theory corrections for the black hole thermodynamics. In particular, we show the emergence of a stable branch of small spherical black holes. We obtain the corrected Hawking-Page transition temperature for black holes with spherical …
We study the first-order $α'$ corrections to the singular 4-dimensional massless stringy black holes studied in the nineties in the context of the Heterotic Superstring. We show that the $α'$ corrections not only induce a non-vanishing mass and give rise to an event horizon, but also eliminate the singularity giving rise to a regular spacetime whose global structure includes further asymptotically flat regions in which the spacetime's mass is positive or negative. We study the timelike and null geodesics and their effective potential, showing that the spacetime is geodesically complete. We dis…
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation function…
We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used to generate the whole spectrum of the solutions. The corresponding spacetime structures, written in terms of the string metric, are analyzed in detail. In particular, we show that only the elementary solutions present naked singularities. The bound states have either null singularities (electric solutions) or are regular (magnetic or dyonic solutions) with …
Higher dimensional Einstein gravity in vacuum admits static black hole solutions with an Einstein manifold of non constant curvature as a horizon. This gives a much richer family of static black holes than in four dimensional GR. However, as we show in this paper, the Gauss-Bonnet string theory correction to Einstein gravity poses severe limitations on the geometry of a horizon Einstein manifold. The additional stringy constraints rule out most of the known examples of exotic black holes with a horizon of non constant curvature.
The Maggiore's method (MM), which evaluates the transition frequency that appears in the adiabatic invariant from the highly damped quasinormal mode (QNM) frequencies, is used to investigate the entropy/area spectra of the Garfinkle--Horowitz--Strominger black hole (GHSBH). Instead of the ordinary QNMs, we compute the boxed QNMs (BQNMs) that are the characteristic resonance spectra of the confined scalar fields in the GHSBH geometry. For this purpose, we assume that the GHSBH has a confining cavity (mirror) placed in the vicinity of the event horizon. We then show how the complex resonant freq…
We compute the low energy decay rates of near-extremal three(four) charge black holes in five(four) dimensional N=4 string theory to sub-leading order in the large charge approximation. This involves studying stringy corrections to scattering amplitudes of a scalar field off a black hole. We adapt and use recently developed techniques to compute such amplitudes as near-horizon quantities. We then compare this with the corresponding calculation in the microscopic configuration carrying the same charges as the black hole. We find perfect agreement between the microscopic and macroscopic calculat…
We consider the effect of vacuum polarization around the horizon of a 4 dimensional axionic stringy black hole. In the extreme degenerate limit ($Q_a=M$), the lower limit on the black hole mass for avoiding the polarization of the surrounding medium is $M\gg (10^{-15}÷10^{-11})m_p$ ($m_p$ is the proton mass), according to the assumed value of the axion mass ($m_a\simeq (10^{-3}÷10^{-6})~eV$). In this case, there are no upper bounds on the mass due to the absence of the thermal radiation by the black hole. In the nondegenerate (classically unstable) limit ($Q_a<M$), the black hole always polari…
Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU(3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU(3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exibits then typical sphaleron structur…
The structure of classical spinning particle based on the Kerr-Newman black hole (BH) solution is investigated. For large angular momentum, $|a|>>m$, the BH horizons disappear exposing a naked ringlike source which is a circular relativistic string. It was shown recently that electromagnetic excitations of this string lead to the appearance of an extra axial stringy system which consists of two half-infinite strings of opposite chirality. In this paper we consider the relation of this stringy system to the Dirac equation. We also show that the axial strings are the Witten superconducting strin…
The duality relating near-horizon microstates of black holes obtained as orbifolds of a subset of AdS3 to the states of a conformal field theory is analyzed in detail. The SL(2,R) invariant vacuum on AdS3 corresponds to the NS-NS vacuum of the conformal field theory. The effect of the orbifolding is to produce a density matrix, the temperature and entropy of which coincide with the black hole. For string theory examples the spectrum of chiral primaries agrees with the spectrum of multi-particle BPS states for particle numbers less than of order the central charge. An upper bound on the BPS par…
In the framework of 4D Einstein-Maxwell Dilaton-Axion theory we show how to obtain a family of both unpolarized and polarized S^1XS^2 Gowdy cosmological models endowed with nontrivial axion, dilaton and electromagnetic fields from a solitonic rotating black hole-type solution by interchanging the r and t coordinates in the region located between the horizons of the black hole configuration. We also get a family of Kantowski-Sachs cosmologies with topology R^1XS^2 from the polarized Gowdy cosmological models by decompactifying one of the compact dimensions.
We study a d-dimensional FRW universe, containing a perfect fluid with p = w ρand \frac{1} {d - 1} \le w \le 1, and find a correspondence principle similar to that of Horowitz and Polchinski in the black hole case. This principle follows quite generally from thermodynamics and the conservation of energy momentum tensor, and can be stated along similar lines as in the black hole case: ``When the temperature T of the universe becomes of order string scale the universe state becomes a highly excited string state. At the transition, the entropies and energies of the universe and strings differ by …
The near horizon geometry of a fundamental string wrapped around an S1 reduced to four dimensions is expected to be AdS2 x S2. A probe string analysis suggests a no-force condition indicating supersymmetry, which coincides with the condition that the AdS2 is embedded in AdS3. We therefore consider the bulk string theory in terms of a WZW model on AdS3 following recent proposals by Dabholkar et. al and Giveon et. al. We find that conformal symmetry of the model naturally leads to the no-force constraints obtained from the probes. Moreover, we are able to extract the values of the moduli that ac…
A classical spinning particle based on the Kerr-Newman black hole (BH) solution is considered. For parameters of spinning particles $|a|>>m$, the BH horizons disappear and BH image is drastically changed. We show that it turns into a skeleton formed by two coupled stringy systems. One of them is the Kerr singular ring which can be considered as a circular D-string with an orientifold world-sheet. Analyzing the aligned to the Kerr congruence electromagnetic excitations of this string, we obtain the second stringy system which consists of two axial half-infinite chiral D-strings. These axial str…
The collision of two particles in the background of a Sen black hole is studied. With the equations of motion of the particles, the center-of-mass energy is investigated when the collision takes place at the horizon of a Sen black hole. For an extremal Sen black hole, we find that the center-of-mass energy will be arbitrarily high with two conditions: (1) spin $a\neq 0$ and (2) one of the colliding particles has the critical angular momentum $l_{\text{c}}=2$. For a nonextremal Sen black hole, we show that, in order to obtain an unlimited center-of-mass energy, one of the colliding particles sh…
We discuss issues relating to the topology of Euclidean de Sitter space. We show that in (2+1) dimensions, the Euclidean continuation of the`causal diamond', i.e the region of spacetime accessible to a timelike observer, is a three-hemisphere. However, when de Sitter entropy is computed in a `stretched horizon' picture, then we argue that the correct Euclidean topology is a solid torus. The solid torus shrinks and degenerates into a three-hemisphere as one goes from the `stretched horizon' to the horizon, giving the Euclidean continuation of the causal diamond. We finally comment on the genera…
Seiberg and Witten have discussed a specifically "stringy" kind of instability which arises in connection with "large" branes in asymptotically AdS spacetimes. It is easy to see that this instability actually arises in most five-dimensional asymptotically AdS black hole string spacetimes with non-trivial horizon topologies. We point out that this is a more serious problem than it may at first seem, for it cannot be resolved even by taking into account the effect of the branes on the geometry of spacetime. [It is ultimately due to the {\em topology} of spacetime, not its geometry.] Next, assumi…
We study Lorentzian D-particles in linear dilaton and the two dimensional black hole backgrounds. The D-particle trajectory follows an accelerated trajectory which is smeared by stringy corrections. For the black hole background we find that the portion of the trajectory behind the horizon appears to an asymptotic observer as ghost D-particle. This suggests a way of constructing a matrix model for the Lorentzian black hole background.
We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically…
To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such ``horizon constraints'' allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string theory approach to black hole entropy arises as a special case, lending support to the claim that the mechanism may be ``universal.'' I argue that the relevant degrees of freedom are Goldstone-boson-lik…
We investigate some of the quantum gravity effects on a vacuum created pair of $(D{\bar D})_3$-brane by a non-linear $U(1)$ gauge theory on a $D_4$-brane. In particular we obtain a four dimensional quantum Kerr(Newman) black hole in an effective torsion curvature formalism sourced by a two form dynamics in the world-volume of a $D_4$-brane on $S^1$. Interestingly the event horizon is found to be independent of a non-linear electric charge and the $4D$ quantum black hole is shown to describe a degenerate vacua in string theory. We show that the quantum Kerr brane universe possesses its origin i…
Motivated by gauge/gravity group in the low energy effective theory of the heterotic string theory and novel aspects of massive gravity in the context of lattice physics, the minimal coupling of Gauss-Bonnet-massive gravity with Born-Infeld electrodynamics is considered. At first, the metric function is calculated and then the geometrical properties of the solutions are investigated. It is found that there is an essential singularity at the origin and the intrinsic curvature is regular elsewhere. In addition, the effects of massive parameters are studied and black hole solutions with multi hor…
Schwarzschild-de Sitter black holes have two horizons that are at different temperatures for generic values of the black hole mass. Since the horizons are out of equilibrium the solutions do not admit a smooth Euclidean continuation and it is not immediately clear what role they play in the gravitational path integral. We show that Euclidean SdS is a genuine saddle point of a certain constrained path integral, providing a consistent Euclidean computation of the probability $\sim e^{-(S_{dS}-S_{SdS})}$ to find a black hole in the de Sitter bath.
The attractor mechanism implies that the supersymmetric black hole near horizon solution is defined only in terms of the conserved charges and is therefore independent of asymptotic moduli. Starting only with the near horizon geometry, Sen's entropy functional formalism computes the entropy of an extreme black hole by means of a Legendre transformation where the electric fields are defined as conjugated variables to the electric charges. However, traditional Euclidean methods require the knowledge of the full geometry to compute the black hole thermodynamic quantities. We establish the connect…
We study string theory on $\mathbb{R}^d\times \mathbb{S}^1$. For applications to thermodynamics, the circumference of the $\mathbb{S}^1$ is the inverse temperature, $β$. We show that for $d=6$, the low energy effective field theory at the inverse Hagedorn temperature, $β=β_H$, has a one parameter family of normalizable spherically symmetric solutions that break the winding symmetry around the $\mathbb{S}^1$. The resulting backgrounds exhibit an enhanced symmetry, with the symmetry breaking pattern $SU(2)_L\times SU(2)_R\to SU(2)_{\rm diagonal}$. The effective field theory analysis of these bac…
This is an introductory, up-to-date review of the essentials of black hole thermodynamics. The main topics surveyed are: (i) the four laws of thermodynamics as applied to a black hole horizon, and the current status of their proofs; (ii) different definitions of horizons, and their unique properties; (iii) the nature of black hole entropy, its quantum and stringy corrections, and ultimate origin from quantum gravity microstates; (iv) the focusing law for the area/entropy; and finally (v) the holographic principle, and how we can use it to learn about the information inside black holes.
