The geometry of null rotation identifications

The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, supersymmetric dilatonic waves and one possible resolution of its singularity in terms of nullbranes are also discussed.Comment: 1+18 pages, 5 figures. v2 references adde

Global Aspects of T-Duality, Gauged Sigma Models and T-Folds

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to T-duality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.Comment: Minor corrections and addition

Spinorial geometry and Killing spinor equations of 6-D supergravity

We solve the Killing spinor equations of 6-dimensional (1,0)-supergravity coupled to any number of tensor, vector and scalar multiplets in all cases. The isotropy groups of Killing spinors are Sp(1)\cdot Sp(1)\ltimes \bH (1), U(1)\cdot Sp(1)\ltimes \bH (2), Sp(1)\ltimes \bH (3,4), $Sp(1) (2)$, $U(1) (4)$ and $\{1\} (8)$, where in parenthesis is the number of supersymmetries preserved in each case. If the isotropy group is non-compact, the spacetime admits a parallel null 1-form with respect to a connection with torsion the 3-form field strength of the gravitational multiplet. The associated vector field is Killing and the 3-form is determined in terms of the geometry of spacetime. The Sp(1)\ltimes \bH case admits a descendant solution preserving 3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If the isotropy group is compact, the spacetime admits a natural frame constructed from 1-form spinor bi-linears. In the $Sp(1)$ and U(1) cases, the spacetime admits 3 and 4 parallel 1-forms with respect to the connection with torsion, respectively. The associated vector fields are Killing and under some additional restrictions the spacetime is a principal bundle with fibre a Lorentzian Lie group. The conditions imposed by the Killing spinor equations on all other fields are also determined.Comment: 34 pages, Minor change

Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics

A generic nonparaxial model for pulse envelopes is presented. Classic Schro¨dinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A wide range of effects, analogous to those in special relativity, then follows for both linear and nonlinear systems. Explicit demonstration is presented through exact bright and dark soliton pulse solutions

Birkhoff's Theorem for Three-Dimensional AdS Gravity

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual Coussaert-Henneaux spacetimes, with isometry groups SO(2) x SO(2,1) or SO(2) x SO(2).Comment: 11 pages, RevTeX4; minor typos corrected, Ref. added, accepted for publication in Phys. Rev.

Composite fluxbranes with general intersections

Generalized composite fluxbrane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold which contains a product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are defined up to a set of functions H_s obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions H_s for intersections related to semisimple Lie algebras is suggested. This conjecture is valid for Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with the components of the dual Weyl vector in the basis of simple roots. Explicit formulas for A_1 + ... + A_1 (orthogonal), "block-ortogonal" and A_2 solutions are obtained. Certain examples of solutions in D = 11 and D =10 (II A) supergravities (e.g. with A_2 intersection rules) and Kaluza-Klein dyonic A_2 flux tube, are considered.Comment: 19 pages, Latex, 1 reference (on a pioneering paper of Gibbons and Wiltshire) and two missing relations are added Published: Class. Quantum Grav. 19 (2002) 3033-304

Trapped surfaces, horizons and exact solutions in higher dimensions

A very simple criterion to ascertain if (D-2)-surfaces are trapped in arbitrary D-dimensional Lorentzian manifolds is given. The result is purely geometric, independent of the particular gravitational theory, of any field equations or of any other conditions. Many physical applications arise, a few shown here: a definition of general horizon, which reduces to the standard one in black holes/rings and other known cases; the classification of solutions with a (D-2)-dimensional abelian group of motions and the invariance of the trapping under simple dimensional reductions of the Kaluza-Klein/string/M-theory type. Finally, a stronger result involving closed trapped surfaces is presented. It provides in particular a simple sufficient condition for their absence.Comment: 7 pages, no figures, final version to appear in Class. Quantum Gra

Branes in Time-Dependent Backgrounds and AdS/CFT Correspondence

We study supergravity solutions of Dp-branes in the time-dependent orbifold background. We show that worldvolume theories decouple from the bulk gravity for p less than six. Along AdS/CFT correspondence, these solutions could provide the gravity description of noncommutative field theory with time-dependent noncommutative parameter. Type II NS5-brane (M5-brane) in the presence of RR n-form for n=0,..., 4 (C field) in this time-dependent background have also been studied.Comment: 15 pages, latex file, v2: typos corrected, ref added, v3: references added, minor change