Three-dimensional Black String Research Articles

Analytic approach to the formation of a three-dimensional black string from a dust cloud

In three-dimensional low-energy string theory,we study the formation of a black string from a dust cloud.We analytically obtain two distinct classes of exact solutions with arbitrary functionsresponsible for mass distributions ofthe dust cloud. The first and second kinds of solutions may describe collapsing dusts butthe first kind is only for inhomogeneous dust distribution while the second kind has a homogeneous limit.The finite collapse time and the Israel junction conditions tell us thatthe first kind solution describesa desired collapsing phenomenon, whereasthe scale factor in the inner spacetime for the second kindturns out to be trivial.In the first kind solution, specific collapsing models can be realized by choosing anappropriate inhomogeneousdust distribution consistent with the Israel junction conditions.Consequently, the inhomogeneous dust cloud eventually collapses to theblack string although the homogeneous dust clouddoes not guarantee the formation of the black string in our setting.The space-like curvature singularities occur at the finite collapse time andthey can be cloaked by the horizon of the black string.

Non-Abelian T-duality of AdS_{dle 3} families by Poisson-Lie T-duality

We proceed to investigate the non-Abelian T-duality of AdS_{2}, AdS_{2}times S^1 and AdS_{3} physical backgrounds, as well as the metric of the analytic continuation of AdS_{2} from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the AdS families as backgrounds of non-linear sigma -models on two- and three-dimensional Lie groups. By considering the Killing vectors of these metrics and by taking into account the fact that the subgroups of isometry Lie group of the metrics can be taken as one of the subgroups of the Drinfeld double (with Abelian duals) we look up the PL T-duality. To construct the dualizable metrics by the PL T-duality we find all subalgebras of Killing vectors that generate subgroup of isometries which acts freely and transitively on the manifolds defined by aforementioned AdS families. We then obtain the dual backgrounds for these families of AdS in such a way that we apply the usual rules of PL T-duality without further corrections. We have also investigated the conformal invariance conditions of the original backgrounds (AdS families) and their dual counterparts. Finally, by using the T-duality rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of BTZ black hole up to two-loop by dualizing on the coordinates varphi and t. When the dualizing is implemented by the shift of direction varphi , we show that the horizons and singularity of the dual spacetime are the same as in charged black string derived by Horne and Horowitz without alpha '-corrections, whereas in dualizing on the coordinate t we find a new three-dimensional black string whose structure and asymptotic nature are clearly determined. For this case, we show that the T-duality transformation changes the asymptotic behavior from AdS_3 to flat.

Integrable λ-deformations of the Euclidean black string

Non-trivial outer algebra automorphisms may be utilized in λ-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT SU(2)k×U(1)/U(1)q with a vector and axial residual gauge. Besides the integer level k and the deformation parameter λ, these models are characterized by the embedding parameter q of the U(1) factor. We show that an axial-vector T-duality persists along the deformations and, therefore, the models are canonically equivalent. We demonstrate integrability even though the space is non-symmetric and compute the RG-flow equations for the parameters λ and q. Our example provides an integrable deformation of the gravitational solution representing a Euclidean three-dimensional black string.

Asymptotic symmetries of three-dimensional black strings

We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global u(1) generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system.

Large-DGravity and Low-DStrings

We show that in the limit of a large number of dimensions a wide class of nonextremal neutral black holes has a universal near-horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains the properties of massless scalars found recently in the large-D limit. For black branes with string charges, the near-horizon geometry is that of the three-dimensional black strings of Horne and Horowitz. The analogies between the α' expansion in string theory and the large-D expansion in gravity suggest a possible effective string description of the large-D limit of black holes. We comment on applications to several subjects, in particular to the problem of critical collapse.

Formation of three-dimensional black strings from gravitational collapse of dust cloud

We study the formation of black strings from a gravitational collapse of cylindrical dust clouds in the three-dimensional low-energy string theory. New junction conditions for the dilaton as well as two junction conditions for metrics and extrinsic curvatures between both regions of the clouds are presented. As a result, it is found that the collapsing dust cloud always collapses to a black string within a finite collapse time, and then a curvature singularity formed at origin is cloaked by an event horizon. Moreover, it is also shown that the collapse process can form a naked singularity within finite time, regardless of the choice of initial data.

Entropy count for extremal three-dimensional black strings

We compute the entropy of extremal black strings in three dimensions, using Strominger's approach to relate the Anti-de-Sitter near-horizon geometry and the conformal field theory at the asymptotic infinity of this geometry. The result is identical to the geometric Bekenstein–Hawking entropy. We further discuss an embedding of three-dimensional black strings in N=1 D=10 supergravity and demonstrate that the extremal strings preserve 1/4 of supersymmetries.

Stability analysis and absorption cross section in three-dimensional black string

It is shown that all string fields except dilaton are non-propagating in the (2+1)-dimensional black string. One finds that the perturbation around the black string reveals a mixing between the dilaton and other fields. Under the new gauge(dilaton gauge), we disentangle this mixing and obtain one decoupled dilaton equation. It turns out that this black string is stable. From the scattering of dilaton off the neutral black string(N=0), we find the absorption cross-section. Further the absorption cross-section for minimally coupled scalar is obtained and we compared it with that of dilaton.

Three-dimensional black holes and string theory

The exact decay rate for emission of massless minimally coupled scalar fields by a non-extremal black hole in 2+1 dimensions is obtained. At low energy, the decay rate into scalars with zero angular momentum is correctly reproduced within conformal field theory. The conformal field theory has both left- and right-moving sectors and their contribution to the decay rate is associated naturally with left and right temperatures of the black hole.

Two-dimensional black hole in the three-dimensional black string.

We discuss the two-dimensional black hole in the (2+1)-dimensional black string. When the charge of the black string Q=0 and thus the torsion ${\mathit{H}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}\mathrm{\ensuremath{\rho}}}$ vanishes, a black string with double horizons becomes a simple product of a two-dimensional (2D) black hole with a single horizon and R. It is shown that the two propagating modes are the dilaton and tachyon in a 3D black string background, and L=h-\ensuremath{\varphi} and the tachyon in a 2D black hole \ensuremath{\bigotimes}R background. We also calculate the reflection and transmission coefficients for the scattering of string fields off 2D black holes. Using the Bogoliubov transformation we find the Hawking temperature from the reflection coefficient of the tachyon.

GAUGING SL(2, R) AND SL(2, R)×U(1) BY THEIR NILPOTENT SUBGROUPS

We consider the gauging of SL(2, R) and SL(2, R)×U(1) WZNW model by their nilpotent subgroups. The resulting space-times of the corresponding sigma models are seen to collapse to the one-dimensional Liouville theory in the first case, and lead to an extremal three-dimensional black string in the second case. We show that these results are also obtained by boosting the Witten black hole solution and Horne and Horowitz black string solution respectively.

O(1, 1) × O(1, 1) Transformations and the Axial and Vector Gaugings in Three-Dimensional Black String

The O(1, 1) ×O(1, 1) transformations are applied to the three-dimensional charged black string solution in the (SL(2, R) ×R)/U(1) WZW model and several classes of background solutions are generated. We analyze the interrelations among them and show how the initial charged axial gauging solution is changed into the uncharged vector gauging one through the O(1, 1) ×O(1, 1) transformation. The solutions connected with the vector gauging are shown to be separated into two parts which are mapped to each other by the simple inversion transformation.

O(1, 1) xO(1, 1) Transformations and the Axial and Vector Gaugings in Three-Dimensional Black String

O(1, 1) xO(1, 1) Transformations and the Axial and Vector Gaugings in Three-Dimensional Black String

Symmetries of string-effective action and spacetime geometry

A two-dimensional charged black hole solution is obtained by implementing a (2,2) transformation on the three-dimensional black string solution. Two different monopole backgrounds in five dimensions are related through an O(2,2) transformation. It has been shown in these examples that the particular O(2,2) transformation corresponds to a duality transformation.

$O(\bar{d}, \bar{d})$ TRANSFORMATIONS AND 3D BLACK HOLE

We generalize the results of a previous paper by one of the authors to show a relationship among a class of string solutions through [Formula: see text] transformations. The results are applied to a rotating black hole solution of three-dimensional general relativity discussed recently. We extend the black hole solution to string theory and show its connection with the three-dimensional black string with nonzero momentum through an [Formula: see text] transformation of the above type.

Target space structure of a chiral gauged Wess-Zumino-Witten model

The background for string propagation is obtained by a chiral gauging of the SL(2, R ) Wess-Zumino-Witten model. It is shown explicitly that the resulting background fields satisfy the field equations of the three-dimensional string effective action and the target space has curvature singularity. Close connection of our solution with the three-dimensional black string is demonstrated.