A two charge system in string theory preserving eight supercharges can be described as a small black hole that has zero entropy in the supergravity approximation, but classical higher derivative corrections produce a finite entropy in accordance with the prediction of microstate counting. On the other hand for the same system one can construct smooth horizonless classical solutions whose geometric quantization describes the individual microstates which contribute to the entropy. In this note we point out that there is no duality frame in which the system admits both these classical descriptions. Thus in a given duality frame horizonless classical solutions and small black holes are not alternate descriptions of the same system; their contributions must be added to get a duality invariant result for the macroscopic degeneracy. We discuss the significance of this observation for the macroscopic computation of the degeneracy of BPS states for a general system. We also discuss the relationship between the degeneracy and the index computation and address the puzzle regarding absence of small black holes in toroidally compactified type II string theory.
We develop a new hybrid WKB technique to compute boundary-to-boundary scalar Green functions in asymptotically-AdS backgrounds in which the scalar wave equation is separable and is explicitly solvable in the asymptotic region. We apply this technique to a family of six-dimensional $\frac{1}{8}$-BPS asymptotically AdS$_3\,\times\,$S$^3$ horizonless geometries that have the same charges and angular momenta as a D1-D5-P black hole with a large horizon area. At large and intermediate distances, these geometries very closely approximate the extremal-BTZ$\,\times\,$S$^3$ geometry of the black hole, …
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…
We construct the first family of horizonless supergravity solutions that have the same mass, charges and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well-approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the hologra…
We outline a systematic procedure to obtain horizonless microstate geometries that have the same charges as three-charge five-dimensional black holes with a macroscopically-large horizon area and an arbitrarily-small angular momentum. There are two routes through which such solutions can be constructed: using multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So far the only solutions corresponding to microstate geometries for black holes with no angular momentum have been obtained via superstrata, and multi-center Gibbons-Hawking spaces have been believed to give rise …
It has been suggested by A. Sen that the entropy of two-charge supersymmetric bound states in string theory should be accounted for by adding the entropy of source-free horizonless supergravity solutions to the entropy associated with the horizons of small black holes. This would imply that the entropy arises differently depending on the duality frame: in the D1-D5 frame one would count source-free horizonless solutions, while in the NS1-P frame one would compute the area of a horizon. This might lead to the belief that the microstates are described by fuzzball solutions in the D1-D5 duality f…
The hoop conjecture, introduced by Thorne almost five decades ago, asserts that black holes are characterized by the mass-to-circumference relation $4π{\cal M}/{\cal C}\geq1$, whereas horizonless compact objects are characterized by the opposite inequality $4π{\cal M}/{\cal C}<1$ (here ${\cal C}$ is the circumference of the smallest ring that can engulf the self-gravitating compact object in all azimuthal directions). It has recently been proved that a necessary condition for the validity of this conjecture in horizonless spacetimes of spatially regular charged compact objects is that the mass…
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…
We derive a non-BPS linear ansatz using the charged Weyl formalism in string and M-theory backgrounds. Generic solutions are static and axially-symmetric with an arbitrary number of non-BPS sources corresponding to various brane, momentum and KKm charges. Regular sources are either four-charge non-extremal black holes or smooth non-BPS bubbles. We construct several families such as chains of non-extremal black holes or smooth non-BPS bubbling geometries and study their physics. The smooth horizonless geometries can have the same mass and charges as non-extremal black holes. Furthermore, we fin…
在不假设任何kappa规范固定的情况下，构造了AdS 5 × S 5共形规范空间中IIB超弦的无穷多个守恒非定域荷，并证明了它们满足超Yangian代数.所得的代数与我们以前的工作相同，其中假设一个特殊的规范，使得Noether流满足平坦性条件。然而，AdS空间上超弦的Noether流的平坦性条件一般是不成立的。我们发现，反常的贡献被吸收到当前的费米子约束起着至关重要的作用，和由此产生的保守的非局域电荷有不同的表达式满足相同的超杨代数。
Hamada and Shiu have recently shown that tree level amplitudes in QED satisfy an infinite hierarchy of soft photon theorems, the first two of which are Weinberg and Low's theorems respectively. In this paper we propose that in tree level massless QED, this entire hierarchy is equivalent to a hierarchy of (asymptotic) conservation laws. We prove the equivalence explicitly for the case of sub-subleading soft photon theorem and give substantial evidence that the equivalence continues to hold for the entire hierarchy. Our work also brings out the (complimentary) relationship between the asymptotic…
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…
We consider the classical static soliton solutions of the Skyrme model with false vacuum potential. We make use of fully three-dimensional relaxation calculations to construct global energy minimizers in the sectors of topological degrees from $Q=1$ to $Q=6$. These solutions may be metastable, they contain a domain of true vacuum inside the core. Further, we explore small regions of negative topological charge density which appear for the Skyrmions of degrees $Q=3,5,6$.
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.
We discuss the continuous and infinitesimal gauge, supergauge, reparameterization, nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries and derive corresponding nilpotent charges for the one (0+1)-dimensional (1D) massive model of a spinning relativistic particle. We exploit the theoretical potential and power of the BRST and supervariable approaches to derive the (anti-)BRST symmetries and coupled (but equivalent) Lagrangians for this system. In particular, we capture the off-shell nilpotency and absolute anticommutatvity of the conserved (anti-)BRST charges within the framewor…
In this paper we propose that bubbles of AdS within Minkowski spacetime, stabilized at a finite radius by stiff matter and an electromagnetic gas, can be an alternative endpoint of gravitational collapse. The bubbles are horizonless with a size up to 12.5% larger than their Schwarzschild radius depending on their charge. We argue that they are stable against small perturbations, and have thermodynamical properties similar to those of real black holes. We provide a realization of the bubbles within string theory that relies on a specific brane intersection giving rise to a shell carrying dissol…
We extend the previous analysis of (locally) asymptotically flat solutions of Kaluza-Klein (KK) theory by assuming that the dilaton charge is an independent parameter. This corresponds to a general nondegenerate matrix of charges within the geodesic sigma model approach and comes into contact with singular solutions of the four-dimensional Einstein-scalar theory. New features of the degenerate class of solutions, which includes regular KK black holes, are also revealed. Solving the constraint equation, we find three distinct branches of the dilaton charge as a function of the other asymptotic …
We present the construction of several microstate geometries of the supersymmetric D1-D5-P black hole in which, within six-dimensional supergravity, the momentum charge is carried by a vector field. The fully backreacted geometries are smooth and horizonless: They are asymptotically AdS$_3 \times S^3$ with an AdS$_2$ throat that smoothly caps off. We propose a holographic dual for these bulk solutions and discuss their extension to asymptotically flat space. In addition, we present several uplifts of the full six-dimensional supersymmetric ansatz to ten-dimensions. In particular, we show that …
We find a plethora of new analytic black holes and globally regular horizonless spacetimes in three dimensions. The solutions involve a single real scalar field $ϕ$ which always admits a magnetic-like expression proportional to the angular coordinate. The new metrics, which satisfy $g_{tt}g_{rr}=-1$ and represent continuous generalizations of the BTZ one, solve the equations of Einstein gravity corrected by a new family of densities (controlled by unconstrained couplings) constructed from positive powers of $(\partial ϕ)^2$ and certain linear combinations of $R^{ab} \partial_a ϕ\partial_b ϕ$ a…
We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primar…
We analyze the Hawking evaporation process of Reissner-Nordström black holes. It is shown that the characteristic radiation quanta emitted by the charged black holes may turn near-extremal black-hole spacetimes into horizonless naked singularities. The present analysis therefore reveals the intriguing possibility that the semi-classical Hawking evaporation process of black holes may violate the fundamental Penrose cosmic censorship conjecture.
A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological consta…
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 re-examine Hawking radiation for a nonrotating (2+1)-dimensional BTZ black hole and evaluate the transmission probability of tunneling through the barrier of the event horizon employing the standard method of WKB approximation. Our results are presented for both uncharged and charged cases. We also explore the associated thermodynamics in terms of Hawking temperature and provide estimates of black hole parameters like the surface gravity and entropy.
